Im, Man Kyu; Kim, Jae-Hee Stochastic calculus for analogue of Wiener process. (English) Zbl 1178.60028 J. Korea Soc. Math. Educ., Ser. B, Pure Appl. Math. 14, No. 4, 335-354 (2007). Summary: We define an analogue of generalized Wiener measure and investigate its basic properties. We define (Itô type) stochastic integrals with respect to the generalized Wiener process and prove the Itô 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. Cited in 1 Document MSC: 60G15 Gaussian processes 60H05 Stochastic integrals 93E11 Filtering in stochastic control theory 60G35 Signal detection and filtering (aspects of stochastic processes) Keywords:generalized Wiener process; stochastic integral; Itô formula; stochastic differential equation; linear filtering PDFBibTeX XMLCite \textit{M. K. Im} and \textit{J.-H. Kim}, J. Korean Soc. Math. Educ., Ser. B, Pure Appl. Math. 14, No. 4, 335--354 (2007; Zbl 1178.60028)