Ee?anueeee oi?aa?neoao

?iai? Oa?ana Oaa/aiea

EIAAEUe*OE TH??e Ieaen?eiae/

OAeE 519.21

E?AEIA? CAAeA*?

C AEIAAeEIAEIE II*AOEIAEIE OIIAAIE

? OOIEOe?IIAEUeI? ?ssAeE

?C I?INOI??A I?E?*A

01.01.05 — oai??y eiia??iinoae

oa 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 ia eaoaae?? oai??? eiia??iinoae oa iaoaiaoe/ii?
noaoenoeee Ee?anueeiai oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea.

Iaoeiaee ea??aiee:

Io?oe?ei? iiiiaioe:

I?ia?aeia i?aai?caoe?y: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

EICA*AIEI TH??E AANEEUeIAE*,

Ee?anueeee oi?aa?neoao ?i. Oa?ana Oaa/aiea,

caa?aeoth/ee eaoaae?ith.

— aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

NIEIOeAA NA?A?E IEAEN?EIAE*,

Iaoe?iiaeueiee oaoi?/iee oi?aa?neoao “Ee?anueeee iie?oaoi?/iee
?inoeooo”, eaoaae?a ia?eaoeiao;

— eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe, aeioeaio

NOAAEIAA IEAIA AIEIAeEIE??AIA,

Ee?anueeee aeiiii?/iee ?inoeooo iaiaaeaeiaioo, eaoaae?a aeui?
iaoaiaoeee.

?inoeooo e?aa?iaoeee ?i. A.I. Aeooeiaa IAI Oe?a?ie, i. Ee?a.

Caoeno a?aeaoaeaoueny “21” /a?aiy 1999 ?. i 14.00 aiaeei? a aoae.
? 42 ia can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 26.001.37 i?e
Ee?anueeiio oi?aa?neoao? ?i. Oa?ana Oaa/aiea ca aae?anith: 252127, i.
Ee?a, i?iniaeo aeaaeai?ea Aeooeiaa, 6, iaoai?ei-iaoaiaoe/iee oaeoeueoao.

C aeena?oaoe??th iiaeia iciaeiieoenue a a?ae?ioaoe? Ee?anueeiai
oi?aa?neoaoo ?i. Oa?ana Oaa/aiea (i. Ee?a, aoe. Aieiaeeie?nueea, 58, e.
10).

Aaoi?aoa?ao ?ic?neaii “17” o?aaiy 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? ?aaee

aeieoi? o?c.-iao. iaoe, i?ioani? Iieey/oe I.I.

Caaaeueia oa?aeoa?enoeea ?iaioe

Aeooaeuei?noue oaie. Aeine?aeaeaiiy aeanoeainoae aeiaaeeiaeo ?yae?a o
??cieo ooieoe?iiaeueieo i?inoi?ao ? iaeiei c aaaeeeaeo iai?yie?a
?icaeoeo oai??? aeiaaeeiaeo i?ioean?a. Iiaeeea?noue cia?aaeaiiy aeayeeo
aeiaaeeiaeo i?ioean?a o aeaeyae? ooieoe?iiaeueieo ?yae?a aeicaiey?
aea/aoe aeanoeaino? oeeo i?ioean?a ia iniia? aeanoeainoae ?o
cia?aaeaiue.

Cie?aia, aeooaeueiei ? ieoaiiy i?i oiiae oa oaeaee?noue ca?aeiino?
noioanoe/ieo ?yae?a o ii?iao ??cieo ooieoe?iiaeueieo i?inoi??a.

C ?ioiai aieo, cia?aaeaiiy aeiaaeeiaeo i?ioean?a o aeaeyae? ca?aeieo
aeiaaeeiaeo ?yae?a a?aee?eaa? aeiaeaoeia? iiaeeeaino? aeey ?o
aeei?enoaiiy ye o nai?e oai??? aeiaaeeiaeo i?ioean?a, oae ? o ??
canoinoaaiiyo a ?ioeo iaoaiaoe/ieo aeenoeeie?iao: i?e ?ica’ycoaaii?
i?aeoe/ieo caaea/ iaoaiaoe/ii? o?ceee c aeiaaeeiaeie ii/aoeiaeie
oiiaaie, iaoaiaoe/iiio iiaeaethaaii? oiui.

Oaeee noai ?a/ae coiiaea inoaii?i /anii iaineaaiee ?ioa?an aeine?aeiee?a
? ?ioaineaiee ?icaeoie oai??? o oeueiio iai?yi?. Iniiae oeueiai iai?yio
aoee caeeaaeai? ua o ?iaioao ?. Iae? (Paley R.), A. C?aioiaea (Zygmund
A.) oa I. A?ia?a (Wiener N.), ? ?icaeioo? o ?iaioao aaaaoueio
aeine?aeiee?a, na?aae yeeo a?aei?oeii i?aoe? oe?a?inueeeo iaoaiaoee?a
I.E.  ssae?aiea, TH.A. Eica/aiea, A.A. Aoeaeea?ia, a oaeiae i?aoe?
Oaeaa?aia (Talagrand M.), ?oi ? I?n?i (Ito K., Nisio M.), Aeaeaeia oa
Ia?eona (Jain N., Markus M.B.).

O 60-? ?iee ii/aeenue aeine?aeaeaiiy ca?aeiino? aeiaaeeiaeo ?yae?a c?
cia/aiiyie o aaiaoiaeo i?inoi?ao. A.A. Aoeaeea?i caeeaa iniiae
caaaeueii? oai??? ca?aeiino? c eiia??i?noth iaeeieoey aeiaaeeiaeo ?yae?a
c iacaeaaeieie /eaiaie c? cia/aiiyie a oiiieia?/ieo i?inoi?ao.

Aeaia oai??y o 70-? ?iee aoea ?icaeiooa ? aeiiiaiaia ?yaeii ?ia?o, o
yeeo aea/aeanue ca?aei?noue ca eiia??i?noth aeiaaeeiaeo ?yae?a ?c
caeaaeieie /eaiaie o ??cieo ooieoe?iiaeueieo i?inoi?ao. Na?aae oeeo
?ia?o a?aei?oeii ?iaioe A.A. Aoeaeea?ia, o yeeo aeine?aeaeo?oueny
ca?aei?noue ca eiia??i?noth aeiaaeeiaeo ?yae?a ?c /eaiaie, ui iaeaaeaoue
aei aaiaoiaeo i?inoi??a, TH.A. Eica/aiea oa ?i., i?enay/aieo aea/aiith
oiia ca?aeiino? aeiaaeeiaeo ?yae?a c caeaaeieie /eaiaie o ii?iao ??cieo
ooieoe?iiaeueieo i?inoi??a.

O oeae /an c’yaeeany cia/ia e?euee?noue ?ia?o, o yeeo aea/aeinue ieoaiiy
i?i oaeaee?noue ca?aeiino? aeiaaeeiaeo ?yae?a o ??aiii??i?e iao?eoe?.
Ianooiiee e?ie o aea/aii? oiia oa oaeaeeino? ca?aeiino? aeiaaeeiaeo
?yae?a aoei c?iaeaii TH.A. Eica/aieii oa ?i. o ?iaioao, a yeeo
?icaeyaeaeany ca?aei?noue aeiaaeeiaeo ?yae?a o ii?iao aeayeeo i?inoi??a
I?e?/a. O ?iaioao TH.A. Eica/aiea, ?.I. Caeaioa?ii? oa A.I.
?ycaioeaai? aoee iaea?aeai? oiiae ca?aeiino? oa caaaeuei? ioe?iee
oaeaeeino? ca?aeiino? aaonniaeo aeiaaeeiaeo ?yae?a o ii?iao aeayeeo
i?inoi??a I?e?/a. Oeeie ae aaoi?aie aoee iaea?aeai? ioe?iee oaeaeeino?
ca?aeiino? o i?inoi?ao I?e?/a aeey noaaaonniaeo aeiaaeeiaeo ?yae?a oa
?yae?a noaaaonniaiai oeio.

Iaea?aeai? caaaeuei? ioe?iee aoee iie?ioai? a ?yae? ?ia?o ia iniia?
iaoiaeo, ui a?oioo?oueny ia ?aea? AE. Eaoaia, nooue yei? iieyaa? a
canoinoaaii? ia??aiino? Aa?iooaeia aeey ciaoiaeaeaiiy oiia ??aiii??ii?
ca?aeiino? aeiaaeeiaeo ?yae?a. Oeae iaoiae aoa cai?iiiiiaaiee TH.A.
Eica/aieii.

Oiiae oa ioe?iee oaeaeeino? ca?aeiino? ca eiia??i?noth aeiaaeeiaeo
?yae?a ciaoiaeyoue oe?iea canoinoaaiiy i?e ?ica’ycaii? caaea/
iaoaiaoe/ii? o?ceee c aeiaaeeiaeie ii/aoeiaeie oiiaaie. O?ce/i?
iinoaiiaee oaeeo caaea/ ?icaeyaeaa Eaiia aea Oa?’?.

O ?iaioao TH.A. Eica/aiea, A.A. Aoeaeea?ia, ?. Aaenaiaa?aa cai?iiiiiaaii
i?aeo?ae, yeee a?oioo?oueny ia aeine?aeaeaii? ca?aeiino? ca eiia??i?noth
o ooieoe?iiaeueieo i?inoi?ao iine?aeiaiino? /anoeiaeo noi, ui
ai?ieneiothoue ?ica’ycie e?aeiai? caaea/?. Oeae i?aeo?ae aoa
aeei?enoaiee aeey iaa?oiooaaiiy canoiniaiino? iaoiaeo Oo?’? aei
?ica’ycaiiy e?aeiai? caaea/? aeey ??aiyiiy a?ia?aie?/iiai oeio c
aeiaaeeiaeie ii/aoeiaeie oiiaaie, a i?eiouaii?, ui aeiaaeeia? oiiae ?
aaonniaeie [Aoeaeea?i A.A., Eica/aiei TH.A.], noi?nii no?iai I?e?/aaeie
[Eica/aiei TH.A., Barrasa de la Krus E.], a oaeiae no?iai noaaaonniaeie
[Eica/aiei TH.A., O?eaoa N.A.] aeiaaeeiaeie i?ioeanaie.

Iaoa aeaii? ?iaioe. Iaoith aeine?aeaeaiue, ?acoeueoaoe yeeo aeeeaaeaii a
aeena?oaoe??, ? iaea?aeaiiy oiia ca?aeiino? oa ioe?iie oaeaeeino?
ca?aeiino? aeayeeo ooieoe?iiaeueieo aeiaaeeiaeo ?yae?a o ii?iao ??cieo
i?inoi??a, a naia i?inoi??a I?e?/a, Lp — i?inoi??a, i?inoi??a Niaie?aa,
a oaeiae iaa?oiooaaiiy canoiniaiino? iaoiaeo Oo?’? aei ?ica’ycaiiy
e?aeiai? caaea/? aeey ??aiyiiy a?ia?aie?/iiai oeio c aeiaaeeiaeie
ii/aoeiaeie oiiaaie, a i?eiouaii?, ui aeiaaeeia? oiiae ? noi?nii no?iai
sub((() aeiaaeeiaeie i?ioeanaie.

Iaoiaee aeine?aeaeaiiy aacothoueny ia ?ic?iaeaiiio TH.A. Eica/aieii
i?aeoiae? aei aeine?aeaeaiiy oiia oa oaeaeeino? ca?aeiino? o ii?iao
??cieo i?inoi??a aeiaaeeiaeo ?yae?a, a oaeiae ca?aeiino? o
ooieoe?iiaeueieo i?inoi?ao iine?aeiaiino? /anoeiaeo noi, ui
ai?ieneiothoue ?ica’ycie e?aeiaeo caaea/ iaoaiaoe/ii? o?ceee c
aeiaaeeiaeie ii/aoeiaeie oiiaaie.

Iaoeiaa iiaecia ?acoeueoao?a ?iaioe.

Iaea?aeaii:

oiiae oa ioe?iee oaeaeeino? ca?aeiino? no?iai sub((() aeiaaeeiaeo
?yae?a o ii?iao i?inoi??a Lp(();

oiiae oa ioe?iee oaeaeeino? ca?aeiino? no?iai sub((() aeiaaeeiaeo
?yae?a o ii?iao i?inoi??a I?e?/a;

oiiae ?nioaaiiy ocaaaeueiaiiai ?ica’yceo e?aeiai? caaea/? aeey
iaeii??aeiiai a?ia?aie?/iiai ??aiyiiy c ii/aoeiaeie oiiaaie, ye? ?
no?iai sub((() aeiaaeeiaeie i?ioeanaie.

ioe?iee oaeaeeino? ca?aeiino? cia?aaeaiue oeueiai ?ica’yceo, io?eiaieo
iaoiaeii Oo?’?, a ii?iao i?inoi??a Niaie?aa.

Oai?aoe/ia oa i?aeoe/ia oe?ii?noue aeena?oaoe??. Iaea?aeai? ?acoeueoaoe
ocaaaeueiththoue ? aeiiiaiththoue a?aeiia?aei? aeine?aeaeaiiy a oai???
aeiaaeeiaeo ?yae?a oa a oai??? e?aeiaeo caaea/ iaoaiaoe/ii? o?ceee.

Oe? ?acoeueoaoe iiaeooue aooe aeei?enoaieie i?e ?ica’ycoaaii? ?yaeo
caaea/ iaoaiaoe/ii? o?ceee, ye? caiaeyoueny aei e?aeiaeo caaea/ c
aeiaaeeiaeie ii/aoeiaeie oiiaaie.

Iniaenoee aianie caeiaoaa/a. Ii oai? aeena?oaoe?? iioae?eiaaii 10 ?ia?o.
Iaoaiaoe/i? ?acoeueoaoe ?ia?o [7-10] iaea?aeai? caeiaoaa/ai naiino?eii.
A aeaieo ?iaioao ni?aaaoi?o iaeaaeeoue aea?? iai?yieo aeine?aeaeaiue oa
iaaiai?aiiy oai?aoe/ieo ?acoeueoao?a. ?acoeueoaoe ?aooe ?ia?o io?eiai?
caeiaoaa/ai naiino?eii.

Ai?iaaoe?y ?iaioe. Iniiai? ?acoeueoaoe aeena?oaoe?eii? ?iaioe
aeiiia?aeaeeny ia nai?ia?? c oai??? eiia??iinoae oa iaoaiaoe/ii?
noaoenoeee iaoai?ei-iaoaiaoe/iiai oaeoeueoaoo Ee?anueeiai oi?aa?neoaoo
?iai? Oa?ana Oaa/aiea, ia I’yo?e oa Oino?e i?aeia?iaeieo eiioa?aioe?yo
?iai? aeaaeai?ea I. E?aa/oea a?aeiia?aeii o o?aai? 1996 ? a o?aai? 1997
?ieo o i. Ee?a?, a oaeiae i?aaenoaaeai? ia Ae?oa?e
Neaiae?iaai-Oe?a?inuee?e eiioa?aioe?? c iaoaiaoe/ii? noaoenoeee (8-13
/a?aiy 1997 ?, i. Oiai, Oaaoe?y).

Ioae?eaoe??. Ii oai? aeena?oaoee? iioae?eiaaii 10 ?ia?o, c ieo 6 ?ia?o
naiiai aaoi?a, 6 ?ia?o iaae?oeiaaii a i?ia?aeieo iaoeiaeo aeaeaiiyo.

Ianya oa no?oeoo?a aeena?oaoe??. Aeena?oaoe?y neeaaea?oueny c anooio,
o?ueio ?icae?e?a, aeniiaeo oa nieneo oeeoiaaii? e?oa?aoo?e, yeee
i?noeoue 67 iaeiaioaaiue. Caaaeueiee ianya ?iaioe ( 110 noi??iie
iaoeiiieniiai oaenoo.

CI?NO ?IAIOE

O anooi? iaa?oioiao?oueny aeooaeuei?noue oaie aeena?oaoe??,
oi?ioeth?oueny iaoa aeine?aeaeaiue, ei?ioei aiae?cothoueny iniiai?
i?aoe?, ui a?aeiinyoueny aei oaie aeena?oaoe??, iaaiaeyoueny iniiai?
iaea?aeai? ?acoeueoaoe.

O ia?oiio ?icae?e? aeena?oaoe?? “I?ino?? sub((() oa n?i’y no?iai
sub((() aeiaaeeiaeo aaee/ei” aaiaeyoueny iiiyooy no?iai sub((() n?i’?
aeiaaeeiaeo aaee/ei ? no?iai sub((() aeiaaeeiaeo i?ioean?a. Oe? iiiyooy
? ocaaaeueiaiiyi iiiyoue a?aeiia?aeii no?iai noaaaonniaeo aeiaaeeiaeo
aaee/ei oa no?iai noaaaonniaeo i?ioean?a. Aeey ieo iaaiaeeoueny ?yae
aaaeeeaeo ?acoeueoao?a, ye? aeei?enoiaothoueny aeey aeiaaaeaiiy oai?ai
ae?oaiai ?icae?eo.

O i?ae?icae?e? 1.1 iaaaaeai? aeaye? a?aeii? ?acoeueoaoe c oai???
i?inoi??a I?e?/a oa i?inoi??a sub(((), a oaeiae noi?ioeueiaai?
aeiiii?aei? oaa?aeaeaiiy, ye? noinothoueny aeanoeainoae N — ooieoe?e
I?e?/a ? aeei?enoai? o ianooiieo i?ae?icae?eao.

O i?ae?icae?e? 1.2 aaaaeai? ianooii? iiiyooy:

Icia/aiiy 1.6. N?i’y ( aeiaaeeiaeo aaee/ei ( ?c i?inoi?o sub((()
iaceaa?oueny no?iai sub(((), yeui ?nio? noaea N(>0, oaea, ui aeey
aoaeue-yei? ia a?eueo i?ae ce?/aiii? iiiaeeie I (i ( (, i ( I ? aeey
aoaeue-yeeo (i ( R1 aeeiio?oueny ia??ai?noue

Noaeo N( aoaeaii iaceaaoe aecia/aeueiith noaeith n?i’? (.

Icia/aiiy 1.7. Aeiaaeeiaee i?ioean

X = {X(t), t ( T }

?c sub((() iaceaa?oueny no?iai sub(((), yeui n?i’y aeiaaeeiaeo aaee/ei
{X(t), t(T} ? no?iai sub((().

N?i’y aeiaaeeiaeo i?ioean?a Xi = {Xi(t), t(T, i(I } iaceaa?oueny noi?nii
no?iai sub(((), yeoi n?i’y aeiaaeeiaeo aaee/ei {Xi(t), t(T, i(I } ?
no?iai sub((().

Aecia/aeueio noaeo n?i’? {Xi(t), t(T, i(I } aoaeaii iaceaaoe
aecia/aeueiith noaeith n?i’? i?ioean?a Xi, i(I.

Iaaaaeai? oaeiae i?eeeaaee noi?nii no?iai sub((() aeiaaeeiaeo i?ioean?a
oa aeaye? aeiiii?aei? oaa?aeaeaiiy.

iioeea. Aeey iaio aeiaaee?a iaea?aeai? oiiae oa ioe?iee oaeaeeino?
ca?aeiino? aeiaaeeiaeo ?yae?a o ii?iao i?inoi??a Lp, e??i oiai, aeey
ae?oaiai aeiaaeeo ( oiiae oa ioe?iee oaeaeeino? ca?aeiino? ?yae?a o
ii?iao i?inoi??a I?e?/a.

O i?ae?icae?e? 2.1 aea/athoueny ?iciiae?ee eaaae?aoe/ieo oi?i a?ae
no?iai sub((() aeiaaeeiaeo aaee/ei ?c i?inoi??a sub((().

( iioeea.

( iaia?a?aia ? no?iai iiiioiiia. Iaoae (*(u) ( N-ooieoe?y,
aeiaeaoeiaa aei ((u).

Oiae? ?nio? oaea noaea (>0, ui i?e an?o (>0 aeeiio?oueny ia??ai?noue

A ( neiao?e/ia iaa?ae’?iii aecia/aia iao?eoey.

Oiae? aeey an?o s >1 aeeiio?oueny ia??ai?noue

aea ( ( noaea, caaeaia a eai? 2.1.

— oaiooa, ? ((x)/x2 ( 0 i?e x ( (.

Oiae? aeey aoaeue-yeeo s > 0 ni?aaaaeeeaa ia??ai?noue:

— aaeoi?, eiiiiiaioe yeiai iaeaaeaoue n?i’? (, ((x) ( N-ooieoe?y
I?e?/a, aeey yei? aeeiiothoueny oiiae eaie 2.3, A — neiao?e/ia
iaa?ae’?iii aecia/aia iao?eoey.

Oiae? aeey aoaeue-yeeo s > 0 ni?aaaaeeeaa ia??ai?noue:

O i?ae?icae?e? 2.2 ?icaeyaeathoueny eeane iine?aeiaiinoae ooieoe?e, aeey
yeeo aeeiiothoueny ia??aiino? oeio Aa?iooaeia.

Iaoae ((,((,() ? (S,(S,() — aei??i? i?inoi?e, ( (() ? ((() — (-ne?i/aii?
i??e; Z — aeayeee aaiao?a i?ino?? aei??ieo ooieoe?e ia i?inoi??
((,((,(), c ii?iith||·||Z; L2(S) — i?ino?? ooieoe?e, ?ioaa?iaaieo c
eaaae?aoii a?aeiinii i??e ((();

yeui ?niothoue:

c L2(S);

i?e aoaeue-yeiio n > 0 aeeiio?oueny ia??ai?noue

? ianooiia iniiaia oaa?aeaeaiiy.

. sseui aeey (-iaeaea an?o s

? aeey (-iaeaea an?o (

oi

O i?ae?icae?e? 2.3 ciaeaeaii oiiae oa oaeaee?noue ca?aeiino? no?iai
sub((() aeiaaeeiaeo ?yae?a o ii?iao i?inoi??a I?e?/a.

aea (S,(S,() — aei??iee i?ino??, qk(s) — iine?aeiai?noue ooieoe?e c
L2(S), a cn — /eneiaa iine?aeiai?noue, aeey yei? aeeiio?oueny
ia??ai?noue c icia/aiiy 2.1.

— iine?aeiai?noue aeiaaeeiaeo aaee/ei c no?iai sub((() n?i’? ( c
aecia/aeueiith noaeith N( (icia/aiiy 1.6); aeey N-ooieoe?? ((x)
aeeiiothoueny i?eiouaiiy oai?aie 2.1.

Iicia/eii

— aeayea /eneiaa iine?aeiai?noue.

aeeiio?oueny

Oiae?

— ooieoe?y, aeiaeaoeiaa aei ((o).

I?e oeueiio aeey aoaeue-yeiai (>0 aeeiio?oueny ia??ai?noue

aea

a ( aecia/aia a eai? 2.1.

I?e ( >1 aeeiio?oueny ia??ai?noue

Aeae? o oeueiio i?ae?icae?e? noi?ioeueiaaii ?yae aaaeeeaeo iane?aee?a c
oe??? oai?aie.

O i?ae?icae?e? 2.4 aea/athoueny oiiae oa oaeaee?noue ca?aeiino?
aeiaaeeiaeo ?yae?a aeaeyaeo

iaia?a?aia ? oaea, ui

Aeey oaeeo ?yae?a ciaeaeaii oiiae oa oaeaee?noue ca?aeiino? o ii?iao
i?inoi??a Lp. Iniiaiei ?acoeueoaoii oeueiai i?ae?icae?eo ? oai?aia 2.4,
yea a?oioo?oueny ia oaa?aeaeaii? oai?aie 2.2.

O o?aoueiio ?icae?e? “Canoinoaaiiy iaoiaeo Oo?’? aei e?aeiaeo caaea/ c
aeiaaeeiaeie ii/aoeiaeie oiiaaie” aeeeaaeaii oaa?aeaeaiiy, ye?
iaa?oioiaothoue canoinoaaiiy iaoiaeo Oo?’? aei e?aeiaeo caaea/ aeey
iaeii??aeiiai a?ia?aie?/iiai ??aiyiiy c ii/aoeiaeie oiiaaie o aeaeyae?
noi?nii no?iai sub((() aeiaaeeiaeo i?ioean?a.

Iniiaiei ?acoeueoaoii oeueiai ?icae?eo ? oaea oai?aia.

Oai?aia 3.2. Iaoae aeiaaeeia? i?ioeane ((x) ? ((x) — noi?nii no?iai
sub((() c aecia/aeueiith noaeith N(, N-ooieoe?y ((x) caaeiaieueiy? oiiae
oai?aie 2.1.

aeey yei? ca?aa?oueny ?yae

I?e oeueiio aeey aoaeue-yeiai ( >0 aeeiio?oueny ia??ai?noue

aea

B — aeayea noaea.

Aai i?e ( >1 aeeiio?oueny ia??ai?noue

Iiae?aia oai?aia noi?ioeueiaaia aeae? aeey aeiaaeeo, eiee aeeiiothoueny
oiiae oai?aie 2.4.

E??i oiai, o o?aoueiio ?icae?e? i?e aeayeeo ii/aoeiaeo i?eiouaiiyo
noi?ioeueiaai? c?o/i?o? ioe?iee ?nioaaiiy ocaaaeueiaiiai ?ica’yceo
?icaeyiooi? caaea/?, ?, ia ?o iniia?, iaea?aeai? oiiae a oa?i?iao
ei??aeyoe?eieo ooieoe?e i?ioean?a ((x) ? ((x), i?e yeeo aeeiiothoueny
oiiae caaaeaieo oai?ai.

Iniiai? ?acoeueoaoe ?iaioe.

Iaea?aeaii:

Oiiae oa ioe?iee oaeaeeino? ca?aeiino? no?iai sub((() aeiaaeeiaeo ?yae?a
o ii?iao i?inoi??a Lp;

Oiiae oa ioe?iee oaeaeeino? ca?aeiino? no?iai sub((() aeiaaeeiaeo ?yae?a
o ii?iao i?inoi??a I?e?/a;

Oiiae ?nioaaiiy ocaaaeueiaiiai ?ica’yceo e?aeiai? caaea/? aeey
iaeii??aeiiai a?ia?aie?/iiai ??aiyiiy c ii/aoeiaeie oiiaaie, ye? ?
no?iai sub((() aeiaaeeiaeie i?ioeanaie;

Ioe?iee oaeaeeino? ca?aeiino? cia?aaeaiue oeueiai ?ica’yceo, io?eiaieo
iaoiaeii Oo?’?, o ii?iao i?inoi??a Niaie?aa.

Iniiai? ?acoeueoaoe aeena?oaoe??

iioae?eiaai? a ianooiieo ?iaioao

Eiaaeue/oe TH.I. I?i oaeaee?noue ca?aeiino? aeiaaeeiaeo ?yae?a o
i?inoi?ao I?e?/a // V I?aeia?iaeia Iaoeiaa Eiioa?aioe?y ?i. aeaae. I.
E?aa/oea. Oace aeiiia?aeae. — Ee?a, 1996. —

N. 189.

Eiaaeue/oe TH.I. I?i ca?aei?noue no?iai sub((() aeiaaeeiaeo ?yae?a o
ii?i? i?inoi?o Lp(U) // Aeooaeuei? ieoaiiy no/anii? iaoaiaoeee ?
o?ceee. Ca. iaoe.

i?aoeue. — I?aeei: IAeI? ?i. I.A. Aiaiey, 1996. — N. 9-12.

Eiaaeue/oe TH.I. Oiiae ca?aeiino? no?iai sub((() aeiaaeeiaeo ?yae?a o
ii?iao i?inoi?o Lp // A?niee Ee?anueeiai oi?aa?neoaoo. Na??y:
o?ceei-iaoaiaoe/i? iaoee. Aei. 1. — E.: Ee?anueeee oi?aa?neoao ?i.
Oa?ana Oaa/aiea, 1996. — N. 72-82.

Eiaaeue/oe TH.I. Aei ieoaiiy i?i ca?aei?noue no?iai sub((() aeiaaeeiaeo
?yae?a o i?inoi?ao I?ee/a // VI I?aeia?iaeia Iaoeiaa Eiioa?aioe?y ?i.
aeaae. I. E?aa/oea. Iaoa??aee eiioa?aioe??. — Ee?a, 1997. — N. 201.

Eiaaeue/oe TH.I. Oiiae ca?aeiino? no?iai sub((() aeiaaeeiaeo ?yae?a o
ii?iao i?inoi??a I?ee/a // A?niee Ee?anueeiai oi?aa?neoaoo. Na??y:
o?ceei-iaoaiaoe/i? iaoee. Aei. 2. — E.: Ee?anueeee oi?aa?neoao ?i.
Oa?ana Oaa/aiea, 1997. — N. 35—39.

Kovalchuk Yu. O. The Boundary-Value Problems for Equations of
Mathematical Physics with Strictly suboe(() Random Initial Conditions
// The Second Scandinavian-Ukrainian Conference in Mathematical
Statistics. Abstracts. — Sweden, Umea. — 1997. — P. 45.

Eica/aiei TH.A., Eiaaeue/oe TH.I. I?i ca?aei?noue o i?inoi?ao I?ee/a
aeayeeo aeiaaeeiaeo ?yae?a // Iaoeia? caienee I?aeeinueeiai
iaae?inoeoooo ?i. I.A. Aiaiey. — 1996. — O. XVI, aei. 1. —

N. 16-20.

Eica/aiei TH.A., Eiaaeue/oe TH.I. I?i ca?aei?noue no?iai sub((()
aeiaaeeiaeo ?yae?a a ii?iao i?inoi??a I?e?/a // Aeiiia?ae? IAI Oe?a?ie.
— 1997. — ?11. — N. 12-15.

Eica/aiei TH.A., Eiaaeue/oe TH.I. E?aaaua caaea/e ni neo/aeiuie
ia/aeueiuie oneiaeyie e ooieoeeiiaeueiua ?yaeu ec sub((() I //
Oe?aeineee iaoaiaoe/aneee aeo?iae. — 1998. — o.50, ?4. — N. 504-515.

Eica/aiei TH.A., Eiaaeue/oe TH.I. E?aaaua caaea/e ni neo/aeiuie
ia/aeueiuie oneiaeyie e ooieoeeiiaeueiua ?yaeu ec sub((() II //
Oe?aeineee iaoaiaoe/aneee aeo?iae. — 1998. — o.50, ?7. — N. 897-906.

Eiaaeue/oe TH.I. E?aeia? caaea/? c aeiaaeeiaeie ii/aoeiaeie oiiaaie ?
ooieoe?iiaeuei? ?yaee ?c i?inoi??a I?e?/a. — ?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 oa iaoaiaoe/ia noaoenoeea. — Ee?anueeee oi?aa?neoao ?iai?
Oa?ana Oaa/aiea, Ee?a, 1999.

Aeine?aeaeothoueny oiiae oa oaeaee?noue ca?aeiino? aeiaaeeiaeo
ooieoe?iiaeueieo ?yae?a ?c i?inoi??a sub((() o ??ciiiai?oieo ii?iao.
Iaea?aeai? ?acoeueoaoe canoiniaothoueny aei aeine?aeaeaiiy e?aeiai?
caaea/? aeey a?ia?aie?/iiai ??aiyiiy c aeiaaeeiaeie ii/aoeiaeie oiiaaie.

Eeth/ia? neiaa: aeiaaeeia? i?ioeane, aeiaaeeia? ?yaee, i?ino?? I?e?/a,
aeeoa?aioe?aeueia ??aiyiiy a?ia?aie?/iiai oeio, iaoiae Oo?’?.

Eiaaeue/oe TH.A. E?aaaua caaea/e ni neo/aeiuie ia/aeueiuie oneiaeyie e
ooieoeeiiaeueiua ?yaeu ec i?ino?ainoa I?ee/a. — ?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.

Enneaaeiaaiea naienoa neo/aeiuo ?yaeia a ?acee/iuo ooieoeeiiaeueiuo
i?ino?ainoaao yaeyaony iaeiei ec aaaeiuo iai?aaeaiee ?acaeoey oai?ee
neo/aeiuo i?ioeannia. Aiciiaeiinoue i?aaenoaaeaiey iaeioi?uo neo/aeiuo
i?ioeannia a aeaea ooieoeeiiaeueiuo ?yaeia iicaieyao eco/aoue naienoaa
yoeo i?ioeannia ia iniiaaiee naienoa ecia?aaeathueo eo ?yaeia.

A aeenna?oaoeee enneaaeothony oneiaey e nei?inoue noiaeeiinoe neo/aeiuo
ooieoeeiiaeueiuo ?yaeia ec i?ino?ainoa sub((() a ?acee/iuo ii?iao, a
eiaiii i?ino?ainoa I?ee/a, Lp —i?ino?ainoa, i?ino?ainoa Niaieaaa.
Iieo/aiiua ?acoeueoaou i?eiaiythony e enneaaeiaaieth e?aaaie caaea/e
aeey aeia?aiee/aneiai o?aaiaiey ni neo/aeiuie ia/aeueiuie oneiaeyie.

A ia?aii ?acaeaea aeenna?oaoeee i?eaaaeaiu ecaanoiua ?acoeueoaou ec
oai?ee i?ino?ainoa I?ee/a e i?ino?ainoa sub(((), iaiaoiaeeiuo aeey
aeaeueiaeoaai eceiaeaiey iaoa?eaea. Aaaaeaiu oaeaea iiaua iiiyoey
naiaenoaa no?iai sub((() neo/aeiuo aaee/ei e no?iai sub((() neo/aeiiai
i?ioeanna, a oaeaea noi?ioee?iaaiu iniiaiua ooaa?aeaeaiey e i?eaaaeaiu
i?eia?u, iiaeoaa?aeaeathuea oeaeaniia?aciinoue aaaaeaiey yoeo iiiyoee,
ia?yaeo n oaeeie eeannaie, eae, iai?eia?, naiaenoaa no?iai i?ee/aauo
neo/aeiuo aaee/ei e no?iai i?ee/aau neo/aeiua i?ioeannu.

auioeea, e aeey neo/ay, eiaaea iia yaeyaony aiaiooie, iineieueeo
aeieacaoaeuenoaa ooaa?aeaeaiee aeey yoeo aeaoo neo/aaa aace?othony ia
?acee/iuo iaoiaeao. Oaeei ia?acii, aeooaeueiie inoaaony i?iaeaia
iaoiaeaeaiey iaoiaea, eioi?ue i?eaiaeee au e aiaeiae/iui ?acoeueoaoai a
iauai neo/aa.

A yoii aea ?acaeaea noi?ioee?iaaii iiiyoea BZ2 — iineaaeiaaoaeueiinoae
ooieoeee, o.a. iiiyoea, iaiauathuaa nouanoaothuea ii?aaeaeaiey ?acee/iuo
eeannia iineaaeiaaoaeueiinoae ooieoeee, aeey eioi?uo auiieiythony
ia?aaainoaa oeia Aa?iooaeia.

I?eaaaeaiu oaeaea aaaeiua i?eia?u oaeeo eeannia.

auioeea, e aeey neo/ay, eiaaea iia yaeyaony aiaiooie.

I?aaenoaaeaiea neo/aeiuo i?ioeannia a aeaea noiaeyueony neo/aeiuo ?yaeia
ioe?uaaao iiaua aiciaeiinoe aeey ?aoaiey caaea/ iaoaiaoe/aneie oeceee ni
neo/aeiuie ia/aeueiuie oneiaeyie. Yoa eaeay auea iieiaeaia a iniiaaiea
aeaeueiaeoeo enneaaeiaaiee, ?acoeueoaou eioi?uo eceiaeaiu a o?aoueai
?acaeaea aeenna?oaoeee.

Iniiaiuie ?acoeueoaoaie o?aoueaai ?acaeaea yaeythony oai?aiu, a eioi?uo
onoaiiaeaiu oneiaey nouanoaiaaiey iaiauaiiiai ?aoaiey e?aaaie caaea/e
aeey iaeii?iaeiiai aeia?aiee/aneiai o?aaiaiey, anee ia/aeueiuie
oneiaeyie yoie caaea/e yaeythony niaianoii no?iai sub((() neo/aeiua
i?ioeannu. I?e yoii iieo/aiu ioeaiee nei?inoe noiaeeiinoe ?yaeia,
i?aaenoaaeythueo yoi ?aoaiea.

Eeth/aaua neiaa: neo/aeiua i?ioeannu, neo/aeiua ?yaeu, i?ino?ainoai
I?ee/a, aeeooa?aioeeaeueiia o?aaiaiea aeia?aiee/anaiai oeia, iaoiae
Oo?uea.

Kovalchuk Yu.O. The boundary-value problems with random initial
conditions and functional series from Orlich spaces. — Manuscript.

Thesis for a degree of Candidate of Science (Ph.D.) in Physics and
Mathematics, speciality 01.01.05. — Probability theory and Mathematical
Statistics. — Kiev Shevchenko University, Kiev, 1999.

Conditions for convergence and estimates of the convergence rate of
random functional series from sub((() spaces in various norms, are
studied. The results obtained are used to investigation of the
boundary-value problem for hyperbolic equation with random initial
conditions.

Key words: random processes, random series, Orlich space, hyperbolic
differential equation, Fourier method.

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