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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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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: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
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. , 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: Theoretical Mathematics and Pedagogical Mathematics

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