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  • 한국과학기술정보연구원(KISTI) 서울분원 대회의실(별관 3층)
  • 2024년 07월 03일(수) 13:30
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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.14 No.4

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STOCHASTIC CALCULUS FOR ANALOGUE OF WIENER PROCESS

Stochastic Calculus for Analogue of Wiener Process

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2007, v.14 no.4, pp.335-354
Im, Man-Kyu (DEPARTMENT OF MATHEMATICS, HANNAM UNIVERSITY)
Kim, Jae-Hee (DEPARTMENT OF MATHEMATICS, HANNAM UNIVERSITY)
Im, Man-Kyu, & Kim, Jae-Hee. (2007). STOCHASTIC CALCULUS FOR ANALOGUE OF WIENER PROCESS. 한국수학교육학회지시리즈B:순수및응용수학, 14(4), 335-354.

Abstract

In this paper, we define an analogue of generalized Wiener measure and investigate its basic properties. We define (<TEX>${\hat}It{o}$</TEX> type) stochastic integrals with respect to the generalized Wiener process and prove the <TEX>${\hat}It{o}$</TEX> formula. The existence and uniqueness of the solution of stochastic differential equation associated with the generalized Wiener process is proved. Finally, we generalize the linear filtering theory of Kalman-Bucy to the case of a generalized Wiener process.

keywords
generalized Wiener process, stochastic integral, <tex> ${\hat}It{o}$</tex> formula, stochastic differential equation, linear filtering

한국수학교육학회지시리즈B:순수및응용수학

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