bog`liq tajribalar ketma-ketligi markov zanjir

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1576496255.doc ) ( ) ( 2 ) ( 1 ,..., , s k s s a a a s s ) 1 ( + s ) 1 ( + s j a s s 1 e 2 e 1 - k e k e a 1 + a 1 - b b b a a a ,..., 2 , 1 , + + ) , ( z b a î p q 1 e k e 1 e k e 2 e 1 - k e i i e ... , , 3 2 1 t t t s t i j i j s ) 1 ( + s j a ij p ÷ ÷ ÷ ÷ ÷ ø ö ç ç ç ç ç è æ = kk k k k k p p p p p p p p p ... ... ... ... ... ... ... …

vodorot atomida elektronlar ma`lum bir orbita bo`yicha aylanadi. elektronning -orbita bo`yicha aylanishini bilan belgilasak, electron o`z orbitasini momentlarda o`zgartiradi. biz elektronning momentda orbitadan, -orbitaga o`tish ehtimoli faqat va larga bog`liq va elektronning oldin qanday orbitada bo`lganligiga bog`liq emas deb faraz qilamiz. elektronlarning bunday harakati ham markov zanjiriga misol bo`ladi. biz bundan keyin saddalik uchun -tajribada hodisa ro`y berishi shartli ehtimolligi tajriba tartib raqamiga bog`liq emas deb faraz qilamiz va bu ehtimollikni o`tish ehtimoli deb ataymiz va uni kabi belgilaymiz. bunday markov zanjiriga bir jinsli markov zanjiri deyiladi. bir jinsli markov zanjiri uchun bir holatdan ikkinchisiga o`tishning to`la ehtimolligi tasnifi quyidagicha matritsa yordamida beriladi. . bu matritsaga o`tish matritsasi deyiladi. daydi zarrachaning harakat qonuni bir jinsli markov zanjiriga misol bo`ladi. uning o`tish matritsasini tuzamiz. o`tish ehtimollari matritsasi elementlari quyidagi shartlarni qanoatlantirishi kerak. 1˚. uning elementlar ehtimolliklar bo`lgani uchun bo`lishi kerak. 2˚. -tajribada holatda bo`lgan sistema -tajribada holatlarning biriga o`tish kerak, ya`ni …

qo`shish aksiomasiga asosan bo`lib, ko`paytirish teoremasiga asosan . , ekanligini hisobga olsak, element matritsaning -satr elementlarining matritsa -ustun elementlariga mos ravishda ko`paytirib qo`shishdan hosil bo`lganligi uchun, matritsalarni ko`paytirish qoidasiga ko`ra o`rinli bo`ladi. agar deb olinsa, (1) dan bo`ladi. ga bir qadamda o`tish matritsasi deyiladi. buni e`tiborga olsak (3) xususiy holda ga ega bo`lamiz. agar har qadamda o`tish matritsasi berilgan bo`lsa, markov zanjiri berilgan deyiladi. bir jinsli markov zanjiri uchun o`rinli bo`ladi. bu tenglikdan foydalanib keltirilgan 1-misol uchun ikki qadamda o`tish matritsasini topish mumkin. isbotsiz quyidagi teoremani keltiramiz. teorema. agar qandaydir uchun o`tish matritsasining barcha elementlari musbat bo`lsa, ga bog`liq bo`lmagan shunday o`zgarmaslar mavjud bo`ladi ( ) va tenglik o`rinli bo`ladi. _1303309935.unknown _1303312190.unknown _1303313054.unknown _1306056002.unknown _1306122310.unknown _1306122406.unknown _1306122502.unknown _1306122529.unknown _1306122548.unknown _1306122521.unknown _1306122496.unknown _1306122337.unknown _1306122220.unknown _1306122294.unknown _1306056057.unknown _1303313890.unknown _1303314558.unknown _1303317060.unknown _1303317107.unknown _1303317125.unknown _1303317083.unknown _1303317007.unknown _1303314123.unknown _1303313097.unknown _1303313827.unknown _1303313082.unknown _1303312964.unknown _1303313012.unknown _1303313027.unknown _1303312985.unknown _1303312903.unknown _1303312940.unknown _1303312457.unknown _1303311630.unknown _1303311930.unknown _1303312005.unknown _1303312108.unknown _1303311961.unknown _1303311638.unknown _1303311800.unknown …

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1576496255.doc ) ( ) ( 2 ) ( 1 ,..., , s k s s a a a s s ) 1 ( + s ) 1 ( + s j a s s 1 e 2 e 1 - k e k e a 1 + a 1 - b b b a a a ,..., 2 , 1 , + + ) , ( z b a î p q 1 e k e 1 e k e 2 e 1 - k e i i e ... , , 3 2 1 t t t s t i j i j s ) 1 ( + s j a ij p ÷ ÷ ÷ ÷ ÷ ø …

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