EE?ANUeEEE OI?AA?NEOAO ?IAI? OA?ANA OAA*AIEA

Niaeoi?nueeee ?ai? sseiae/

OAeE 519.21

NOIOANOE*I? ??AIssIIss

A I?INOI?AO OI?IAEUeIEO ?ssAe?A

? OI?IAEUeIEO A?AeIA?AAEAIUe

01.01.05 — oai??y eiia??iinoae

? iaoaiaoe/ia noaoenoeea

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Ee?a — 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia a Iaoe?iiaeueiiio oaoi?/iiio oi?aa?neoao? Oe?a?ie
«Ee?anueeee iie?oaoi?/iee ?inoeooo» I?i?noa?noaa ina?oe Oe?a?ie.

Aeaeaoeueeee TH??e Eueaiae/

Iaoeiaee ea??aiee:

— aeieoi? o?c.-iao. iaoe, i?ioani? Iaoe?iiaeueiee oaoi?/iee
oi?aa?neoao Oe?a?ie «EI?», i?ioani?

Io?oe?ei? iiiiaioe:

— aeieoi? o?c.-iao. iaoe, i?ioani? I?oo?a THe?y Noaiai?aia,

Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea, i?ioani?;

— eaiaeeaeao o?c.-iao. iaoe Eoeee Ieaen?e Ieoaeeiae/,

?inoeooo iaoaiaoeee IAI Oe?a?ie, aeieoi?aio.

I?ia?aeia onoaiiaa: ?inoeooo i?eeeaaeii? iaoaiaoeee oa iaoai?ee IAI
Oe?a?ie, i. Aeiiaoeuee.

Caoeno a?aeaoaeaoueny 21 /a?aiy 1999 ?. ia 11.00 aiaeei? ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee Ae26.001.37 i?e Ee?anueeiio oi?aa?neoao?
?iai? Oa?ana Oaa/aiea ca aae?anith:

252127, i.Ee?a — 127, i?iniaeo aeaae. Aeooeiaa, 6, Ee?anueeee
oi?aa?neoao ?iai? Oa?ana Oaa/aiea, iaoai?ei-iaoaiaoe/iee oaeoeueoao.

C aeena?oaoe??th iiaeia iciaeiieoenue a a?ae?ioaoe? Ee?anueeiai
oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea (aoe. Aieiaeeie?nueea, 58).

Aaoi?aoa?ao ?ic?neaiee 11 o?aaiy 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee Iieey/oe I.I.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE.

Aeooaeueiinoue oaie. Oai??y oi?iaeueieo noaiaiaaeo ?yae?a, oiaoi
noaiaiaaeo ?yae?a aac aeiiae caiaeiinoi — ci?noiaiee oa ia?niaeoeaiee
iai?yiie no/anii? iaoaiaoeee. Oi?iaeueii ?yaee i?e?iaeiei /eiii
aeieeathoue i?e ?ica’ycaii? aaaaoueio i?eeeaaeieo i?iaeai — cie?aia, i?e
canoinoaaiii iaoiaea noaiaiaaeo ?yaeia aeey ?ica’yceo ?ioaa?aeueieo oa
aeeoa?aioeiaeueieo ?iaiyiue c aiaeioe/ieie eiaoioei?ioaie. Oi?iaeuei?
iia?aoi?i? ?yaee ye naiino?eiee aeaaa?a?/iee ia’?eo ?icaeyaeaeenue a
?iaioao Oa?ae?, Ao?aae?, a i?ci?oa — a ?iaioao TH.E. Aeaeaoeueeiai oa
eiai o/i?a.

Iaeiei c iaeaaaeeea?oeo aniaeo?a aeaii? oai??? ?
?ioaa?i-aeeoa?aioe?aeuei? ??aiyiiy a i?inoi?ao oi?iaeueieo noaiaiaaeo
?yae?a. Aeaoa?iiiiaaii aeeoa?aioeiaeueii ?iaiyiiy a i?inoi?ao
oi?iaeueieo iia?aoi?ieo ?yaeia oa a?aeiia?aei? aaiethoe?ei? n?iaenoaa
?icaeyaeaeenue, cie?aia, a ?iaioao TH.E. Aeaeaoeueeiai oa A.I.
Aa?aiiae/a. Aeinoaoii oiiae caiaeiinoi ?yaea ?ica’yceo a
aeaoa?iiiiaaiiio aeiaaeeo, ui oiiaeeeaeththoue canoinoaaiiy iaoiaea
noaiaiaaeo ?yae?a aei aeaoa?i?iiaaieo aeeoa?aioe?aeueieo ??aiyiue c
aiae?oe/ieie eiao?oe??ioaie, iiaeia io?eiaoe ca aeiiiiiaith oai?aie
Eioi-Eiaaeaanueei?. I?ioa ia?aianaiiy ?acoeueoao?a oai???
aeaoa?i?iiaaieo ??aiyiue a i?inoi?ao oi?iaeueieo ?yae?a ia noioanoe/iee
aeiaaeie iia’ycaia n iaaieie o?oaeiiuaie, ui iaoiiaeai? niaoeeo?eith
noioanoe/ieo ?ioaa?ae?a. Noioanoe/i? ??aiyiiy a i?inoi?ao oi?iaeueieo
?yae?a oa oi?iaeueieo a?aeia?aaeaiue ? ? iniiaiei ia’?eoii
aeine?aeaeaiiy aeaii? aeena?oaoe?eii? ?iaioe.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Iniiai?
?acoeueoaoe aeaii? aeena?oaoe?eii? ?iaioe aoee io?eiai? a ?aieao
aeine?aeaeaiue ii iaoeiaei aea?aeathaeaeaoiei oaiai, ui aeeiioaaeanue ia
eaoaae?? iaoaiaoe/ieo iaoiae?a nenoaiiiai aiae?co Ee?anueeiai
iie?oaoi?/iiai ?inoeoooo:

?2794 «Noioanoe/i? aeeoa?aioe?aeuei? ??aiyiiy», 1994-1995 ?iee;

?2028 «Noioanoe/iee aiae?c oa noioanoe/i? ??aiyiiy», 1996-1997 ?iee.

Iaoa ? caaea/? aeine?aeaeaiue.

Io?eiaiiy aeinoaoi?o oiia ?nioaaiiy oa ?aeeiino? aeey ?ica’yceo
noioanoe/ieo ??aiyiue a i?inoi?ao oi?iaeueieo ?yae?a ? oi?iaeueieo
a?aeia?aaeaiue.

?ic?iaea ?aeo?aioii? i?ioeaaeo?e ia/eneaiiy ?ica’yceo ??aiyiue a
i?inoi?ao oi?iaeueieo ?yae?a ? oi?iaeueieo a?aeia?aaeaiue ia aac?
ocaaaeueiaiiy eeane/ii? oi?ioee aa??aoe?? noaei? ia aeiaaeie
noioanoe/ieo ??aiyiue a a?eueaa?oiaiio i?inoi??.

Io?eiaiiy aeinoaoi?o oiia ca?aeiino? ?ica’yceo noioanoe/iiai ??aiyiiy a
i?inoi?? oi?iaeueieo ?yae?a ye noaiaiaaiai ?yaeo ii ii/aoeia?e oiia?;
io?eiaiiy aiaeiao oai?aie Eio?-Eiaaeaanueei? aeey noioanoe/ieo ??aiyiue
a a?eueaa?oiaiio i?inoi??.

Iaoiaee aeineiaeaeaiue. O ?iaioi aeei?enoaii iaoiaee oai???
noioanoe/iiai ?ioaa?oaaiiy oa noioanoe/ieo ??aiyiue a a?eueaa?oiaiio
i?inoi??, a oaeiae caaaeuei? iaoiaee ooieoe?iiaeueiiai aiae?co ia
a?eueaa?oiaeo oa aaiaoiaeo i?inoi?ao.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a. Iniiai? ?acoeueoaoe, io?eiai?
a aeena?oaoe?ei?e ?iaio?, ? iiaeie.

Io?eiaii aiaeia eeane/ii? oi?ioee aa??aoe?? noaei? aeey aeiaaeeo
e?i?eieo noioanoe/ieo ??aiyiue a a?eueaa?oiaiio i?inoi??;

Aeiaaaeaii oai?aie ?nioaaiiy oa ?aeeiino? ?ica’yceo noioanoe/ieo
??aiyiue a i?inoi?ao oi?iaeueieo ?yae?a ? oi?iaeueieo a?aeia?aaeaiue oa
?ic?iaeai ?aeo?aioiee aeai?eoi ia/eneaiiy eiiiiiaio?a ?ica’yceo.

Aeiaaaeaii ia?e?anueeo aeanoea?noue ?ica’yceo noioanoe/ieo ??aiyiue a
i?inoi?? oi?iaeueieo ?yae?a.

Aeiaaaeaii aaiethoe?eio aeanoea?noue ?ica’yceo noioanoe/iiai ??aiyiiy a
i?inoi?? oi?iaeueieo a?aeia?aaeaiue;

Io?eiaii aeinoaoi? oiiae ca?aeiino? noaiaiaaiai ?yaeo ?ica’yceo
noioanoe/iiai ??aiyiiy a i?inoi?? oi?iaeueieo ?yae?a.

Aeiaaaeaii aiaeia oai?aie Eio?-Eiaaeaanueei? aeey noioanoe/ieo ??aiyiue
a a?eueaa?oiaiio i?inoi?? o aeiaaeeo e?i?eii? aeeooc?? ? aiae?oe/iiai a
iaeiio ieie? ioey cnoao, a oaeiae aeey neaey?ieo noioanoe/ieo ??aiyiue c
aiae?oe/ieie a ieie? ioey aeeooc??th oa cnoaii.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. ?acoeueoaoe, io?eiai? a
aeena?oaoe?ei?e ?iaio?, iathoue oai?aoe/ia cia/aiiy.

Aiaeia oi?ioee aa??aoe?? noaei?, aeaaaeaiee aeey e?i?eieo iaiaeii??aeieo
noioanoe/ieo ??aiyiue a a?eueaa?oiaiio i?inoi??, iiaea aooe aeei?enoaiee
aeey aeine?aeaeaiiy oa ?ica’ycaiiy noioanoe/ieo aeeoa?aioe?aeueieo
??aiyiue c /anoeiieie iio?aeieie, cie?aia — a oai??? ea?oaaiiy, i?e
aeine?aeaeaii? iiaaae?iee e?i?eiiai ia’?eoa a noioanoe/iiio na?aaeiaeu?.

Aiaeia oai?aie Eio?-Eiaaeaanueei? aeey noioanoe/ieo ??aiyiue iiaea aooe
aeei?enoaiee aeey aeine?aeaeaiiy oa ?ica’ycaiiy noioanoe/ieo ??aiyiue c
iae?io?oeaaeie ei?o?oe??ioaie, aiae?oe/ieie a aeia?eueii iaeiio ieie?
ioey; oae? ??aiyiiy, ye i?aaeei, iathoue eeoa eieaeueiee ?ica’ycie, ?
cai?iiiiiaaiee iaoiae aea? ciiao io?eiaoe neeueiee eieaeueiee ?ica’ycie
o aeaeyae? noaiaiaaiai ?yaeo ii ii/aoeia?e oiia?.

Io?eiai? ?acoeueoaoe uiaei ?nioaaiiy, ?aeeiino? oa aeanoeainoae
?ica’yceo noioanoe/ieo ??aiyiue a i?inoi?ao oi?iaeueieo ?yae?a ?
oi?iaeueieo a?aeia?aaeaiue iiaeooue aooe aeei?enoai? aeey iiaeaeueoiai
?icaeoeo noioanoe/iiai aiae?co ia oi?iaeueieo aeaaa?a?/ieo no?oeoo?ao.

Iniaenoee aianie caeiaoaa/a. Iniiai? ?acoeueoaoe aeena?oaoe??eii? ?iaioe
io?eiai? aeena?oaioii naiino?eii, i?e iino?ei?e oaac? oa i?aeo?eioe? c
aieo iaoeiaiai ea??aieea.

Ai?iaaoeiy ?iaioe. Iniiaii ?acoeueoaoe aeena?oaoe?eii? ?iaioe
aeiiiaiaeaeeny oa iaaiai?thaaeeny ia iaoeiaiio nai?ia?? eaoaae?e oai???
eiia??iinoae Ee?anueeiai oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea (ea??aiee
nai?ia?o — aeaae. I.E. ssae?aiei), iaoeiaiio nai?ia?? Ee?anueeiai
iie?oaoi?/iiai ?inoeoooo c oai??? aaon?anueeeo i?ioean?a (ea??aiee
nai?ia?o — i?io. A.A. Aoeaeea?i), iaoeiaiio nai?ia?? ?inoeoooo
iaoaiaoeee IAI Oe?a?ie «*eneaiiy Iaeeyaaia oa canoinoaaiiy» (ea??aiee
nai?ia?o — i?io. A.A. Aei?iaiaoeaa), 5-e I?aeia?iaei?e iaoeia?e
eiioa?aioe?? ?i. aeaae. I.E?aa/oea (Ee?a, 1996), Conferenece on
Stochastic Differential and Differentia Equations (Gy(r, Hungaria,
1996), 7-e E?einuee?e iniiiie oeie?-neiiicioi? (Naaanoiiieue, 1996),
Iaaeaeoia?iaeiie eiioa?aioeee ii noioanoe/aneiio e aeiaaeueiiio aiaeeco
(Ai?iiaae, 1997), Iiaeia?iaeiie eiioa?aioei? ii. I.E?aeia ii oai?i?
iia?aoi?ia oa ?? canoinoaaiith (Iaeana, 1997), 7th Vilnius Conference On
Probability Theory And Mathematical Statistics (Vilnius, Lithuania,
1998).

Ioaeieaoei?. Iniiaii ?acoeueoaoe iioaeieiaaii a oanoe noaooyo [1-6] oa
o oacao eiioa?aioei? [7].

No?oeoo?a ? ianya aeena?oaoe??. ?iaioa neeaaea?oueny ?c anooio,
o?ueio ?icae?e?a, aeniiae?a ? nieneo e?oa?aoo?e ?c 51
iaeiaioaaiue. Caaaeueiee ianya ?iaioe 114 noi??iie.

CI?NO ?IAIOE

O anooii iaa?oioiaaii aeai? oaie aeena?oaoei? ia iniiai aiaeico noaio
i?iaeaie, cacia/aia aeooaeueiinoue caaea/i aeineiaeaeaiiy noioanoe/ieo
??aiyiue a i?inoi?ao oi?iaeueieo ?yae?a ? oi?iaeueieo a?aeia?aaeaiue oa
iiaoaeiae ?o ?ica`yceia, iiaeaia caaaeueia oa?aeoa?enoeea iiaecie oa
oai?aoe/ii? oeiiiinoi iaea?aeaieo ?acoeueoaoia.

O ia?oiio ?icaeiei ?icaeyaea?oueny eiiieia noioanoe/ia ?iaiyiiy

( SEQ F \* MERGEFORMAT 1 )

a a?eueaa?oiaiio i?inoi?? Y (an? a?eueaa?oia? i?inoi?e aaaaeathoueny
ae?enieie oa naia?aaaeueieie), aea:

w(t) — a?ia??anueeee i?ino??, anioe?eiaaiee c a?eueaa?oi-oi?aeoiaei
iniauaiiyi H+ ( H0 ( H-;

ooieoei? A i B — ocaiaeaeaii i?ioeane ic cia/aiiyie a L(Y) oa
L(Y,L2(H0,Y)) aiaeiiaiaeii, aeeoa?aioeieiaii i?e eiaeiiio t([0,T] ii
aieiio ooio oa iaiaaeaii ?iaiiii?ii ii t ?acii ic nai?th iioiaeiith ii
aieiio ooio;

f oa g — ocaiaeaeaii i?ioeane ic cia/aiiyie a i?inoi?ao Y i
L(Y,L2(H0,Y)) aiaeiiaiaeii, ani iiiaioe yeeo iaiaaeaii ?iaiiii?ii ii
t([0,T].

Ooo ? aeae? L(B1, B2) iicia/a? i?ino?? e?i?eieo iaia?a?aieo iia?aoi??a,
ui ae?thoue c aaiaoiaa i?inoi?o B1 a aaiao?a i?ino?? B2; L2(B,Y)
iicia/a? i?ino?? a?eueaa?oi-oi?aeoiaeo iia?aoi??a, ui ae?thoue c
aaiaoiaa i?inoi?o B a a?eueaa?o?a i?ino?? Y.

Cacia/eii, ui i?e aeaieo oiiaao aaiethoeieiee iia?aoi? S(t,s)
a?aeiia?aeiiai iaeii??aeiiai ??aiyiiy iiaea ia iaoe iaiaaeaiiai
iaa?iaiiai. ?icaeie iineoue aeiiiiiaeiee oa?aeoa?, iaeiae io?eiaii
?acoeueoaoe iathoue naiinoieia cia/aiiy.

Noioanoe/i? ??aiyiiy oeio ( SEQ f f1 \* MERGEFORMAT 1 )
?icaeyaeaeenue, cie?aia, a ?iaioao TH.E. Aeaeaoeueeiai, aea aoee
aeiaaaeai? oai?aie ?nioaaiiy oa ?aeeiino? ? aeine?aeaeaii ?yae
aeanoeainoae ?ica’yceo. A aeena?oaoe?ei?e ?iaio? aeey ??aiyiue oeio (
SEQ f f1 \* MERGEFORMAT 1 ) iaaiaeeoueny aiaeia a?aeiii? oi?ioee
«aa??aoe?? noaei?».

Oai?aia 1.4. ?ica’ycie ??aiyiiy ( SEQ F f1 \* MERGEFORMAT 1 )
aea?oueny oi?ioeith

,

aea eiao?oe??ioe c1(t) oa c2(t) aecia/athoueny ??aiyiiyie:

, ( SEQ f \* MERGEFORMAT 2 )

. ( SEQ f \* MERGEFORMAT 3 )

iicia/aii iia?aoe?th ?icoe?aiiai ?ioaa?oaaiiy, D iicia/a? iia?aoe?th
aeeoa?aioe?thaaiiy ii a?eiio ooio (noioanoe/iiai aeeoa?aioe?thaaiiy).

Iane?aeie 1. O aeiaaeeo aeaoa?i?iiaaii? aeeooc?? B(t) ?ica’ycie ??aiyiiy
( SEQ f f1 \* MERGEFORMAT 1 ) iiaea?oueny o aeaeyae?:

Iane?aeie 2. sseui ? aeeooc?y B(t) ? cnoa A(t) ? iaaeiaaeeiaeie,
?ica’ycie ??aiyiiy ( SEQ f1 \* MERGEFORMAT 1 ) iaaoaa? aeaeyaeo,
aiaeia?/iiai aei a?aeiii? oi?ioee aa??aoe?? noaei?:

. ( SEQ f \* MERGEFORMAT 4 )

Caoaaaeaiiy 1.1. O aeiaaeeo, yeui noioanoe/i? iio?aei? DA(t) oa DB(t)
iathoue aeaeyae ?ioaa?aeueieo ooieoe?iiae?a a?aeiinii o?a?eoi??e A oa B,
??aiyiiy ( SEQ F f3 \* MERGEFORMAT 2 ) a?aeiinii c2 ? ?ioaa?aeueiei
??aiyiiyi oeio Aieueoa??a ? ia? ?aeeiee ?ica’ycie, a c1 ciaoiaeeoueny ?c
ni?aa?aeiioaiiy ( SEQ f f4 \* MERGEFORMAT 3 ) i?e a?aeiiiio c2.

I?eeeaae 1.1. ?icaeyiaii noioanoe/ia ??aiyiiy

, ( SEQ f \* MERGEFORMAT 5 )

aea:

( — iaa?aeiiee ocaiaeaeaiee i?ioean a aieueaa?oiaiio i?inoi?i Y;

z — ocaiaeaeaiee i?ioean a aieueaa?oiaiio i?inoi?i Z, ui caaeiaieueiy?
noioanoe/iiio ?iaiyiith

; ( SEQ f \* MERGEFORMAT 6 )

ooieoei? A: Z ([0,T] ( L(Y) oa B: Z ([0,T] ( L(Y,L2(H0,Y)) iaiaaeaii
?acii c iioiaeiith ii z(Z;

f oa g — ocaiaeaeai? i?ioeane ic cia/aiiyie a i?inoi?ao Y oa L2(H0,Y)
aiaeiiaiaeii, c iaiaaeaieie ii t iiiaioaie aoaeue-yeiai ii?yaeeo;

ooieoei? ( (t) ( L(Z), ((t) ( L(Z,L2(H0,Z)) iaiaaeaii ia [0,T].

Iaoae U(t,r) (r ( t) — aaiethoe?eiee iia?aoi?, ui a?aeiia?aea? ??aiyiith
( SEQ f f6 \* MERGEFORMAT 6 ). Oiae? ?ica’ycie ??aiyiiy ( SEQ f f5 \*
MERGEFORMAT 5 ) iiaeia iiaeaoe o aeaeyae?

,

aea eiao?oe??ioe c1(t) oa c2(t) aecia/athoueny ??aiyiiyie:

.

Aeae? a ?icae?e? ?icaeyaeathoueny ??aiyiiy oeio ( SEQ f f1 \*
MERGEFORMAT 1 ) c iaaeiaaeeiaeie iia?aoi?aie aeeooc??? oa cnoao,
i?e/iio cnoa, i?e aeiaeaoeia?e aeiic? aeeneiaoeaiino?, ia iiaeiai aooe
iaiaaeaiei. Oai?aie ?nioaaiiy oa ?aeeiino? ?ica’yceo aeey ??aiyiue
oeueiai oeio aeiaaaeai?, cie?aia, TH.E.Aeaeaoeueeei oa N.A.Oii?iei. A
aeena?oaoe?ei?e ?iaio? aeey ??aiyiue aeaiiai oeio aeiaiaeeoueny aiaeia
eeane/ii? oi?ioee aa??aoe?? noaei?.

Oai?aia 1.6. Iaoae a ??aiyii? ( SEQ f f1 \* MERGEFORMAT 1 )
eiao?oe??ioe A oa B ? iaaeiaaeeiaeie, i?e/iio cnoa A(t) ? e?i?eiei,
iiaeeeai iaiaiaaeaiei iia?aoi?ii, ui caaeiaieueiy? aeiiaai:

(A(t)(, ()Y ( 0 (aeeneiaoeai?noue);

( ( 0, t([0,T]: (((A(t)-( idY)-1(( ( C/(1+(),

aea C — eiinoaioa, ui ia caeaaeeoue a?ae t. (Ooo ? aeae? idY iicia/a?
oioiaei?e iia?aoi? a i?inoi?? Y.)

Oiae? ?ica’ycie ??aiyiiy ( SEQ f f1 \* MERGEFORMAT 1 ) iiaea aooe
iiaeaiee o aeaeyae? ( SEQ f var \* MERGEFORMAT 4 ).

sse i?eeeaae iiaeeeaiai canoinoaaiiy oai?aie 1.6, iaaiaeeoueny
noioanoe/ia ??aiyiiy c /anoeiieie iio?aeieie.

I?eeeaae 1.3. Iaoae Y = H0 = L2(G), aea G — iaeanoue a Rn. ?icaeyiaii
noioanoe/ia ??aiyiiy c /anoeiieie iio?aeieie:

aea:

A = (ajk)1 ( j,k ( n — aeiaeaoiuei aecia/aia iao?eoey;

yae?i Kb: [0,T] ( G(3 ( R eaaae?aoe/ii ?ioaa?iaii a [0,T] ( G(3 ii i???
Eaaaaa;

yae?i Kg: [0,T] ( G(2 ( R ?ioaa?iaii a [0,T] ( G(2 ii i??? Eaaaaa a
aoaeue-ye?e noaiai?.

Aeaia ??aiyiiy caaeiaieueiy? aeiiaai oai?aie 1.6 ? ia? ?aeeiee
?ica’ycie, yeee iiaea aooe ciaeaeaiee ca oi?ioeith ( SEQ f var \*
MERGEFORMAT 4 ).

O ae?oaiio ?icae?e? ?icaeyaeathoueny noioanoe/i? ??aiyiiy a i?inoi??
oi?iaeueieo ?yae?a.

Icia/aiiy 2.1. Iaoae B — aaiaoia i?inoi?. Aeiaieueio iineiaeiaiinoue y =
(yk)k ( 0, oaeo ui ( k ( 1: yk(B, iacaaii oi?iaeueiei ?yaeii a i?inoi??
B (y(B((). sseui y0=0, oi?iaeueiee ?yae y aoaeaii iaceaaoe
oeaio?iaaiei.

Icia/aiiy 2.2. Iaoae Y — a?eueaa?o?a, B — aaiao?a i?inoi?e. Aeiaieueio
iineiaeiaiinoue iia?aoi??a a = (ak)k ( 0, oaeo ui ( k ( 1: ak — eiiieiee
iia?aoi? c Y(k a B, a0(B, iacaaii oi?iaeueiei aiaeia?aaeaiiyi, ui aei? c
Y a B. Aoaeaii eacaoe, ui oi?iaeueia aiaeia?aaeaiiy a c Y a B ?
iaia?a?aiei, yeui ( k(1: ak(L(Y(k,B). Aoaeaii eacaoe, ui oi?iaeueia
aiaeia?aaeaiiy a c Y a B ? oeaio?iaaiei, yeui a0 = 0.

I?inoi? oi?iaeueieo aiaeia?aaeaiue c Y a B iicia/a?oueny L((Y,B).

Iaaeae?, yeui ia aeacaii iioa, on? oi?iaeueii aiaeia?aaeaiiy
aaaaeathoueny iaia?a?aieie.

Iaoae Y1, Y2 — a?eueaa?oia? i?inoi?e, B — aaiao?a i?ino??. Aeey
oi?iaeueieo aiaeia?aaeaiue aILY(Y1,Y2) oa bILY(Y2,B), b0 = 0,
aaiaeeoueny iia?aoeiy eiiiiceoei?:

, n(1.

Aeiaiaeeoueny, ui iia?aoeiy eiiiiceoei? anioeiaoeaia.

Aeey oi?iaeueiiai aiaeia?aaeaiiy aILY(Y,B) ? oeaio?iaaiiai oi?iaeueiiai
?yaea y(B(( aaiaeeoueny oi?iaeueiee ?yae a(y)(B((:

, n(1.

Oi?iaeueiee ?yae a(y) ?icaeyaea?oueny ye ?acoeueoao ae?? oi?iaeueiiai
a?aeia?aaeaiiy a ia oi?iaeueiee ?yae y. Iaaeae?, yeui ia aeacaii iioa,
oni oi?iaeuei? ?yaee ? oi?iaeuei? a?aeia?aaeaiiy aaaaeathoueny
iaia?a?aieie oa oeaio?iaaieie.

Aeae? a ?icae?e? aaiaeyoueny noioanoe/ii ?iaiyiiy a i?inoi?i oi?iaeueieo
?yaeia. Iaoae Y — a?eueaa?o?a i?ino??. Ia’?eoii ?icaeyaeo ? ianooiia
?iaiyiiy:

( SEQ f \* MERGEFORMAT 7 )

aea a(t)ILY(Y,Y), b(t)ILY(Y, L2(H0,Y)), y(t) — iaaiaeiiee aeiaaeeiaee
ocaiaeaeaiee i?ioean ic cia/aiiyie a i?inoi?i Y((, ys — ii/aoeiaa oiiaa,
aeii?ia aiaeiinii (-aeaaa?e Fs=((w((),0((\(s). Aaaaea?oueny, ui ooieoe??
an oa bn ? aei??ieie iaiaaeaieie a?aeia?aaeaiiyie c [0,T] a L(Y(n,Y) oa
L(Y(n, L2(H0,Y)) a?aeiia?aeii.

?iaiyiiy ( SEQ f formal \* MERGEFORMAT 7 ) ?icoii?oueny iieiiiiiaioii,
oiaoi ( SEQ f formal \* MERGEFORMAT 7 ) ca aecia/aiiyi aeaiaaeaioia
nenoaii:

n(1. ( SEQ f \* MERGEFORMAT 8 )

Aeey ?iaiyiiy ( SEQ f formal \* MERGEFORMAT 7 ) aeiaaaeaii inioaaiiy i
?aeei?noue ?ica’yceo, a oaeiae ia?e?anueea aeanoeainoue ?ica’yceo ye
aeiaaeeiaiai i?ioeano a Y((.

Oai?aia 2.5. ??aiyiiy ( SEQ f formal \* MERGEFORMAT 7 ) ia? ?ica’ycie,
?aeeiee c oi/i?noth aei noioanoe/ii? aea?aaeaioiino?.

Oai?aia 2.6. ?ica’ycie ??aiyiiy ( SEQ f formal \* MERGEFORMAT 7 ) ?
ia?e?anueeei i?ioeanii a i?inoi?? Y((.

Aeiaiaeeoueny, ui eiiiiiaioe ?ica’yceo nenoaie ( SEQ f formal_sys \*
MERGEFORMAT 8 ) iiaeia ciaoiaeeoe ?aeo?aioii, ?ica’ycoth/e ia eiaeiiio
e?ioe? e?i?eia iaiaeii??aeia noioanoe/ia ??aiyiiy oeio ( SEQ f f1 \*
MERGEFORMAT 1 ) ca aeiiiiiaith oi?ioee ( SEQ f var \* MERGEFORMAT 4
)/

.

(«aiae?oe/i?noue cnoao»). Iaoae, e?ii oiai, a1(t) oa b1(t) —
aieueaa?oi-oiiaeoiai iia?aoi?e.

Oiaei iniothoue aeaye? eiinoaioe r1,r2 >0 oa iiiaio coieiee (, (>s
iaeaea iaiaaia, oae? ui i?e s(t((:

.

.

Oiaei iniothoue aeaye? eiinoaioe r1,r2 >0 oa iiiaio coieiee (, (>s
iaeaea iaiaaia, oae? ui i?e s(t((:

.

Oaa?aeaeaiiy oai?ai 2.7 oa 2.8 oiiaeeeaeththoue canoinoaaiiy iaoiaea
noaiaiaaeo ?yae?a aei ?ica’yceo noioanoe/ieo ??aiyiue a a?eueaa?oiaiio
i?inoi??.

?icaeyiaii noioanoe/ia ??aiyiiy a a?eueaa?oiaiio i?inoi??:

( SEQ f \* MERGEFORMAT 9 )

aea ((t) — iaa?aeiiee ocaiaeaeaiee i?ioean a a?eueaa?oiaiio Y, A oa B —
aeii?ii iaiaaeaii aiaeia?aaeaiiy c [0,T] ( Y a Y oa a L2(H0,Y)
aiaeiiaiaeii, (s — iaaeiaaeeiaa ii/aoeiaa oiiaa. Aoaeaii aaaaeaoe, ui
A(t,() oa B(t,() — aiaeioe/ii ooieoei? ii ( a ieiei ioey.

Iaoae ooieoeiyi A(t,() oa B(t,() aiaeiiaiaeathoue oi?iaeueii
aiaeia?aaeaiiy a(t)( L(Y), oiaoi:

aeey ( c ?aae?ono aiae?oe/iino?.

Icia/aiiy 2.12. Iaoae ( — iiiaio coieiee, A((t) = A(t)(((t), B((t) =
B(t)(((t), aea (((t) — oa?aeoa?enoe/ia ooieoe?y iiiaeeie {t([0,T]| t (
(}.

Aoaeaii eacaoe, ui ( SEQ f usual \* MERGEFORMAT 9 ) ia? ?ica’ycie
(((t), ui inio? aei iiiaioa coieiee (, yeui i?ioean (((t) ? neeueiei
?ica’yceii ianooiiiai noioanoe/iiai ?iaiyiiy:

.

Iaoae (yn)n(1 — ?ica’ycie ??aiyiiy ( SEQ f formal \* MERGEFORMAT 7 ) c
ii/aoeiaith oiiaith (s oa ei?o?oe??ioaie a(t) oa b(t), ui
a?aeiia?aeathoue ooieoe?yi A(t,() oa B(t,().

Oai?aia 2.9. Iaoae iniothoue aeayei eiinoaioe r1,r2 > 0 i iiiaio coieiee
(, ( >s iaeaea iaiaaia, oaei, ui i?e s ( t ( (:

,

.

Oiae? i?e (((s||Y ( r2 «coieiaiee» i?ioean

,

? ?ica’yceii ( SEQ f usual \* MERGEFORMAT 9 ), ui inio? aei iiiaioa
coieiee (.

I?eeeaae 2.5. Neaey?ia noioanoe/ia ??aiyiiy

( SEQ f \* MERGEFORMAT 10 )

A neeo oai?aie 2.8, ??aiyiiy ( SEQ f usual_example \* MERGEFORMAT 10 )
caaeiaieueiy? aeiiaai oai?aie 2.9. Ioaea, ??aiyiiy ( SEQ f
usual_example \* MERGEFORMAT 10 ) ia? ?ica’ycie aei aeayeiai
aeiaeaoiueiai iiiaioa coieiee, ? oeae ?ica’ycie iiaeia ooeaoe iaoiaeii
noaiaiaaeo ?yae?a.

O ?icae?e? 3 aeiaaaeaii ?nioaaiiy, ?aeei?noue oa aaiethoe?eia
aeanoea?noue ?ica’yceo noioanoe/iiai ??aiyiiy a i?inoi?? oi?iaeueieo
a?aeia?aaeaiue. Iniiaiei ia’?eoii aeine?aeaeaiiy a ?icae?e? ? ??aiyiiy

( SEQ f \* MERGEFORMAT 11 )

aea a(t)ILY(Y,Y), b(t)ILY(Y, L2(H0,Y)), S((,s) — iaaiaeiiee aeiaaeeiaee
ocaiaeaeaiee i?ioean ic cia/aiiyie a i?inoi?i Y((, S(s,s) — ii/aoeiaa
oiiaa, aeii?ia aiaeiinii (-aeaaa?e Fs. Aaaaea?oueny, ui ooieoe?? an oa
bn ? aei??ieie iaiaaeaieie a?aeia?aaeaiiyie c [0,T] a L(Y,Y) oa L(Y,
L2(H0,Y) a?aeiia?aeii.

?iaiyiiy ( SEQ f formal_map \* MERGEFORMAT 11 ) ?icoii?oueny
iieiiiiiaioii, oiaoi ( SEQ f formal_map \* MERGEFORMAT 11 ) ca
aecia/aiiyi aeaiaaeaioia nenoaii:

n(1.

Oai?aia 3.1. Iaoae an oa bn an oa bn ? aei??ieie iaiaaeaieie
a?aeia?aaeaiiyie c [0,T] a L2(Y(n,Y) oa L2(Y(n(H0,Y) a?aeiia?aeii.
Iaoae, aei oiai ae: S1(s,s)-idY ( L2(Y,Y), Sn(s,s) ( L2(Y(n,Y) (n (.2).

Oiae? ??aiyiiy ( SEQ f formal_map \* MERGEFORMAT 11 ) ia? ?aeeiee c
oi/i?noth aei noioanoe/ii? aea?aaeaioiino? ?ica’ycie S(t,s), i?e/iio:
S1(t,s)-idY ( L2(Y,Y), Sn(t,s) ( L2(Y(n,Y) (n (.2).

Oai?aia 3.2. Iaoae aeeiiothoueny aeiiae oai?aie 3.1 oa S(s,s)=IdY, aea
(IdY)1= idY, (IdY)n=0 i?e n (.2 (IdY — oioiaei? oi?iaeueia
a?aeia?aaeaiiy a Y).

Oiae? n?i’y iia?aoi??a S(t,s) (0 ( s ( t ( T) ? aaiethoe?eiith, oiaoi
S(s,s) =IdY, S(t,r)( S(r,s)= S(t,s) i?e s ( r ( t.

Aeniiaee:

ye aeiiii?aeiee ?acoeueoao, iiaoaeiaai noioanoe/iee aiaeia oi?ioee
aa??aoe?? noaei? aeey ?ica’yceo e?i?eieo iaiaeii??aeieo ??aiyiue;

aeiaaaeaii oai?aie inioaaiiy oa ?aeeiino? ?ica`yceia noioanoe/ieo
??aiyiue a i?inoi?ao oi?iaeueieo ?yae?a ? oi?iaeueieo a?aeia?aaeaiue;

aeiaaaeaia ia?e?anueea aeanoea?noue ?ica’yceo noioanoe/iiai ??aiyiiy a
i?inoi?? oi?iaeueieo ?yae?a;

aeiaaaeaia aaiethoe?eia aeanoea?noue ?ica’yceo noioanoe/iiai ??aiyiiy a
i?inoi?? oi?iaeueieo a?aeia?aaeaiue;

io?eiai? aeinoaoi? oiiae ca?aeiino? (i?ioyaii aeiaaeeiaiai ?ioa?aaeo
/ano) aeey ?yaeo ?ica’yceo noioanoe/iiai ??aiyiiy a i?inoi?? oi?iaeueieo
?yae?a;

iiaoaeiaai aiaeia oai?aie Eio?-Eiaaeaanueei? aeey noioanoe/ieo ??aiyiue
a a?eueaa?oiaiio i?inoi?? a aeiaaeeo e?i?eii? aeeooc?? oa aiae?oe/iiai a
ieie? ioey cnoao, a oaeiae aeey neaey?ieo noioanoe/ieo ??aiyiue c
aiae?oe/ieie a ieie? ioey aeeooc??th oa cnoaii;

Iniiaii ?acoeueoaoe aeena?oaoei? iioaeieiaaii a ?iaioao:

Niaeoi?neee E.ss. ssaiay oi?ioea aeey ?aoaiey eeiaeiiai iaiaeii?iaeiiai
noioanoe/aneiai o?aaiaiey// Aeiiia?ae? IAI Oe?a?ie. — 1996. — ?11. —
N.45-52.

Spectorsky I. Stochastic Equations in Formal Mappings// Progress in
Systems and Control Theory. — 1997 — Vol.23: Stochastic Differential and
Difference Equations. — P. 267-272.

Niaeoi?neee E.ss. Iaiauaiea oi?ioeu aa?eaoeee iinoiyiiie aeey eeiaeiiai
iaiaeii?iaeiiai noioanoe/aneiai o?aaiaiey// I?iaeaiu oi?aaeaiey e
eioi?iaoeee. — 1998. — ?5. — C. 107-112.

Niaeoi?neee E.ss. Iaoiae noaiaiiuo ?yaeia aeey noioanoe/aneeo o?aaiaiee
n aiaeeoe/aneeie eiyooeoeeaioaie// Eeaa?iaoeea e nenoaiiue aiaeec. —
1999. — ?2. — C. 133-140.

Spectorsky I. Analog Of Feimann-Kac Formula for Multiplicative
Functional in the Space of Formal Series.// Spectral and Evolutionary
Problems. — Vol.8: Proceedings of the Eighth Crimean Autumn Mathematical
School-Symposium. — P. 151-155.

Spectorsky I. Stochastic Equations and Evolution Families in the space
of Formal Mappings// Spectral and Evolutionary Problems. — Vol.7:
Proceedings of the Seventh Crimean Autumn Mathematical School-Symposium.
— P.124-127.

Spectorsky I. Convergence of Solution of Stochastic Equation in the
Space of Formal Series// 22-nd European Meeting of Stastistisians.7-th
Vilnius Conference on Probability Theory and Mathematical Statistics. —
Vilnius: TEV. — 1998. — P.419-420.

Ei?enooth/enue iaaiaeith, oi/o a?aecia/eoe iino?eio oaaao oa i?aeo?eieo
c aieo iaoeiaiai ea?iaieea aeaaeai?ea IAI Oe?a?ie Aeaeaoeueeiai TH??y
Eueaiae/a, ia?aae/ania nia?oue yeiai ? oyaeeith ao?aoith aeey
a?o/eciyii? oa na?oiai? iaoee.

Niaeoi?nueeee ?.ss. Noioanoe/i? ??aiyiiy a i?inoi?ao oi?iaeueieo ?yae?a
? oi?iaeueieo a?aeia?aaeaiue. — ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.01.05 — oai??y
eiia??iinoae ? iaoaiaoe/ia noaoenoeea. — Ee?anueeee oi?aa?neoao ?iai?
Oa?ana Oaa/aiea, Ee?a, 1999.

Aeena?oaoeith i?enay/aii iiaoaeia? aeaiaio?a oai??? noioanoe/ieo
??aiyiue a i?inoi?ao oi?iaeueieo ?yae?a ? oi?iaeueieo a?aeia?aaeaiue. A
?aieao aeine?aeaeaiue aoee aeiaaaeai? oai?aie ?nioaaiiy oa ?aeeiino?
?ica’yceo noioanoe/ieo ??aiyiue a i?inoi?ao oi?iaeueieo ?yae?a ?
oi?iaeueieo a?aeia?aaeaiue. Ia aac? io?eiaiiai noioanoe/iiai aiaeiaa
oi?ioee «aa??aoe?? noaei?» iiaoaeiaai ?aeo?aioiee aeai?eoi ?ica’ycaiiy
noioanoe/ieo ??aiyiue a i?inoi?ao oi?iaeueieo ?yae?a ? oi?iaeueieo
a?aeia?aaeaiue. Aeey noioanoe/ieo ??aiyiue a i?inoi?? oi?iaeueieo
a?aeia?aaeaiue aeiaaaeaia aaiethoe?eia aeanoea?noue ?ica’yceo. Aeey
noioanoe/ieo ??aiyiue a i?inoi?? oi?iaeueieo ?yae?a aeiaaaeaia
ia?e?anueea aeanoea?noue ?ica’yceo, iiaoaeiaai aiaeia cai?ioiueiai
??aiyiiy Eieiiai?iaa. sse iiaeeeaa canoinoaaiiy, aeiaaaeai aiaeia
oai?aie Eio?-Eiaaeaanueei? aeey noioanoe/ieo ??aiyiue a a?eueaa?oiaiio
i?inoi??.

Eeth/oai neiaa: oi?iaeueiee ?yae, oi?iaeueia a?aeia?aaeaiiy, noioanoe/ia
??aiyiiy a a?eueaa?oiaiio i?inoi??, e?i?eia noioanoe/ia ??aiyiiy,
noioanoe/ia ??aiyiiy c aiae?oe/ieie eiao?oe??ioaie, iaoiae noaiaiaaeo
?yae?a.

Niaeoi?neee E.ss. Noioanoe/aneea o?aaiaiey a i?ino?ainoaao oi?iaeueiuo
?yaeia e oi?iaeueiuo ioia?aaeaiee. — ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.01.05 — oai?ey
aa?iyoiinoae e iaoaiaoe/aneay noaoenoeea. — Eeaaneee oieaa?neoao eiaie
Oa?ana Oaa/aiei, Eeaa, 1999.

Aeenna?oaoeey iinayuaia iino?iaieth yeaiaioia oai?ee noioanoe/aneeo
o?aaiaiee a i?ino?ainoaao oi?iaeueiuo ?yaeia e oi?iaeueiuo ioia?aaeaiee.

Aeenna?oaoeeiiiay ?aaioa aeeth/aao aaaaeaiea, o?e ?acaeaea, auaiaeu e
nienie eeoa?aoo?u ec 51 iaeiaiiaaiey. Iauee iauai ?aaiou ninoaaeyao 114
no?aieoe iaoeiiieniiai oaenoa.

Ai aaaaeaiee iainiiauaaaony auai? oaiu aeenna?oaoeee ia iniiaa aiaeeca
i?iaeaiu, ioia/aaony aeooaeueiinoue caaea/e enneaaeiaaiey e iino?iaiey
?aoaiey noioanoe/aneeo o?aaiaiee a i?ino?ainoaa oi?iaeueiuo ?yaeia e
oi?iaeueiuo ioia?aaeaiee, i?eaiaeeony iauay oa?aeoa?enoeea iiaeciu e
oai?aoe/aneie oeaiiinoe iieo/aiiuo ?acoeueoaoia.

Ia?aue ?acaeae iinayuai iaiauaieth eeanne/aneiai iaoiaea «aa?eaoeee
iinoiyiiie» ia neo/ae eeiaeiiai noioanoe/aneiai o?aaiaiey a
aeeueaa?oiaii i?ino?ainoaa. I?e neo/aeiuo aeeooocee e niina,
niaeaniaaiiuo n aeia?ianeei iioieii (-aeaaa?, ?aoaiea iaiaeii?iaeiiai
noioanoe/aneiai o?aaiaiey naiaeeony e ?aoaieth eioaa?aeueiuo o?aaiaiee
oeia Aieueoa??a, ia niaea?aeaueo noioanoe/aneiai eioaa?aea. I?e
aeaoa?ieie?iaaiiuo eiyooeoeeaioao aeeooocee e niina iieo/aia oi?ioea,
aiaeiae/iay eeanne/aneie oi?ioea aa?eaoeee iinoiyiiie aeey
aeaoa?ieie?iaaiiuo aeeooa?aioeeaeueiuo o?aaiaiee. I?e aeaoa?ieie?iaaiiuo
eiyooeoeeaioao oi?ioea aa?eaoeee iinoiyiiie iaiauaaony ia neo/ae
iaia?aie/aiiiai aeenneiaoeaiiai iia?aoi?a niina.

Iniiaiui iauaeoii ?anniio?aiey ai aoi?ii ?acaeaea yaeyaony
noioanoe/aneia o?aaiaiea a i?ino?ainoaa oi?iaeueiuo (noaiaiiuo) ?yaeia.
Aeey ?anniao?eaaaiuo o?aaiaiee aeieacuaaaony oai?aia nouanoaiaaiey e
aaeeinoaaiiinoe ?aoaiey, aeieacuaaaony ia?eianeia naienoai ?aoaiey,
auaiaeeony aiaeia ia?aoiiai o?aaiaiey Eieiiai?iaa. A neo/aa,
niioaaonoaothuai eeiaeiiio iia?aoi?o aeeooocee e aiaeeoe/aneiio a
iaeioi?ie ie?anoiinoe ioey niino, aeieacuaaaony noiaeeiinoue ?aoaiey eae
noaiaiiiai ?yaea a oiiieiaee aeeueaa?oiaa i?ino?ainoaa aei iaeioi?iai
neo/aeiiai iiiaioa inoaiiaee. A neaey?iii neo/aa oai?aia i noiaeeiinoe
?aoaiey iaiauaaony ia neo/ae, niioaaonoaothuee i?iecaieueiui
aiaeeoe/aneei a ie?anoiinoe ioey eiyooeoeeaioai aeeooocee e niina. Eae
i?eeiaeaiea, aeieacuaaaony aiaeia oai?aiu Eioe-Eiaaeaaneie aeey
noioanoe/aneeo o?aaiaiee a aeeueaa?oiaii i?ino?ainoaa.

A o?aoueai ?acaeaea iniiaiui iauaeoii ?anniio?aiey yaeyaony
noioanoe/aneia o?aaiaiea a i?ino?ainoaa oi?iaeueiuo ioia?aaeaiee.
Oi?iaeueiia ioia?aaeaiea ii?aaeaeyaony eae iineaaeiaaoaeueiinoue
iia?aoi?iuo eiyooeoeeaioia oi?iaeueiiai noaiaiiiai ?yaea e yaeyaony
aiaeiaii aiaeeoe/aneie ooieoeee aac o?aaiaaiee noiaeeiinoe. Aeey
?anniao?eaaaiuo o?aaiaiee aeieacuaaaony nouanoaiaaiea, aaeeinoaaiiinoue
e yaiethoeeiiiia naienoai ?aoaiey eae yeaiaioa a i?ino?ainoaa
oi?iaeueiuo ioia?aaeaiee.

Eeth/aaua neiaa: oi?iaeueiue ?yae, oi?iaeueiia ioia?aaeaiea,
noioanoe/aneia o?aaiaiea a aeeueaa?oiaii i?ino?ainoaa, eeiaeiia
noioanoe/aneia o?aaiaiea, noioanoe/aneia o?aaiaiea n aiaeeoe/aneeie
eiyooeoeeaioaie, iaoiae noaiaiiuo ?yaeia.

Spectorskii I.Ya. Stochastic Equations in the Space of Formal Series and
Formal Mappings. — Manuscript.

Thesis for a Philosophy Doctor degree by speciality 01.01.05 —
Probability theory and mathematical statistics. — Kiev Taras Shevchenko
University, Kiev, 1999.

The dissertation is devoted to construct the elements of theory of
stochastic equations in the spaces of formal series and formal mappings.
We prove theorems for existence and uniqueness of solution to stochastic
equations in the spaces of formal series and formal mappings. Using the
obtained stochastic analogue of «constant variation» formula, we
construct recursive algorithm to solve stochastic equations in the
spaces of formal series and formal mappings. For stochastic equations in
the spaces of formal mappings we prove the evolution property of
solution. For stochastic equations in the spaces of formal series we
prove the Markov property of solution and construct the analogue of the
second Kolmogorov equation. As a possible application, we prove the
analogue of Cauchy-Kovalevskaya theorem for stochastic equations in
Hilbert space.

Keywords: formal series, formal mapping, stochastic equation in Hilbert
space, linear stochastic equation, stochastic equation with analytical
coefficients, method of power series.

Aeaeaoeeee TH.E., Oiiei N.A. Ia?u e aeeooa?aioeeaeueiua o?aaiaiey a
aaneiia/iiia?iii i?ino?ainoaa. — I.: Iaoea, 1983. — 384 n.

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