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Теория случайных функций

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Iineianeee Ainoaea?noaaiiue Einoeooo Yeaeo?iieee e Iaoaiaoeee

(Oaoie/aneee Oieaa?neoao)

EO?NIAAss ?AAIOA

ii eo?no

“Oai?ey neo/aeiuo ooieoeee“

Nooaeaio: Oa?aiaoe Ae.A.

I?aiiaeaaaoaeue: Iaaeaaaeaa A.E.

Aa?eaio: 2.4.5.a

Iineaa, 1995

Aeaii:

Ainnoaiaaeeaaaiay, ?aca?ae?iaaiiay nenoaia (5,1) n EIO, aa?iyoiinoue
n?aaaouaaiey EIO ?aaia b.

A?aiy iaauoiaea ec no?iy (o.a. aacioeaciie ?aaiou) iniiaiiai yeaiaioa
?ani?aaeaeaii yeniiiaioeeaeueii n ia?aiao?ii a.

A?aiy ainnoaiiaeaiey auoaaeoaai ec no?iy yeaiaioa ?ani?aaeaeaii
yeniiiaioeeaeueii n ia?aiao?ii m.

Oei ?aca?ae?iaaiey – iaiaa?oaeaiiue.

Aeey iienaiey ninoiyiey nenoaiu aaaaeai aeaoia?iue neo/aeiue iioeann
n(t) = (x(t), d(t)) n eii?aeeiaoaie, iienuaathueie:

– ooieoeeiie?iaaiea yeaiaioia

x(t) I {0, 1, 2} – /enei iaeni?aaiuo yeaiaioia;

– ooieoeeiie?iaaiea EIO

d(t) I {0,1} – 1, anee eni?aaai, 0 – anee iao.

Oae eae a?aiaia aacioeaciie ?aaiou e ainnoaiiaeaiey eiatho
yeniiiaioeeaeueiia ?ani?aaeaeaiea, oi a neeo naienoa yeniiiaioeeaeueiiai
?ani?aaeaeaiey, iieo/ei, /oi x(t) – iaeii?iaeiue Ia?eianeee i?ioeann.

Ii?aaeaeei ninoiyiea ioeaca nenoaiu:

Nenoaia ioeacuaaao eeai anee ia?aoiaeeo a ninoiyiea 2 i?ioeanna x(t)
(o.a. ioeac eaeiai-eeai yeaiaioa i?e eiee/anoaa ?aca?aiuo yeaiaioia,
?aaiui ioeth), eeai anee iaoiaeeony a ninoiyiee 0 i?ioeanna d(t) (o.a.
ioeac eaeiai-eeai yeaiaioa e ioeac EIO).

Oaeei ia?acii, iiaeii iino?ieoue a?ao ninoiyiee nenoaiu:

0

1

I

0 – ninoiyiea, i?e eioi?ii 0 iaeni?aaiuo yeaiaioia,

o.a. ninoiyiea n(t) = (0, d(t))

1 – ninoiyiea, i?e eioi?ii 1 iaeni?aaiue yeaiaio,

o.a. ninoiyiea n(t) = (1, 1)

I – ninoiyiea, i?e eioi?ii eeai 2 iaeni?aaiuo yeaiaioa, eeai 1
iaeni?aaiue yeaiaio e iaeni?aaiue EIO,

o.a. eiiiiceoeey ninoiyiee n(t) = (1, 1), n(t) =(2, 0) – iiaeiuathuaa
ninoiyiea.

Iaeaeai eioaineaiinoe ia?aoiaeia.

Oae eae auoiae ec no?iy eaaeaeiai ec yeaiaioia – niauoey iacaaeneiua, oi
iieo/ei:

aa?iyoiinoue auoiaea ec no?iy yeaiaioa: 1-exp(-5ah) = 5ah + o(h)

aa?iyoiinoue ainnoaiiaeaiey yeaiaioa: 1-exp(-mh) = mh + o(h)

TH Iieo/ei nenoaio aeeooa?aioeeaeueiuo o?aaiaiee Eieiiai?iaa:

,

.

, oi, iiaenoaaeyy cia/aiey eioaineaiinoae, iieo/aai:

=0)

I?aaenoaaeyy eaaeaeoth ec iieo/aiiuo ooieoeee a aeaea noiiu aeaoo
i?aaeeueiuo ae?iaae, iieo/aai:

:

TH Eneiiay aa?iyoiinoue iaauoiaea nenoaiu ec no?iy ca a?aiy t:

,

aaea

,

Eoae,

,

aaea

Ii?aaeaeei oaia?ue n?aaeiaa a?aiy aeecie oaeie nenoaiu, o.a. MT

(T – a?aiy aeecie nenoaiu):

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