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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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
Kim, Jae-Hee
Im,, M. , & Kim,, J. (2007). Stochastic Calculus for Analogue of Wiener Process. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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