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Stochastic Calculus for Analogue of Wiener Process

김재희|임만규
한국수학교육학회|2007.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제14권 제4호|pp. 335-354

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Abstract

In this paper, we define an analogue of generalized Wiener measure and investigate its basic properties. We define (Itˆo type) stochastic integrals with respect to the generalized Wiener process and prove the Itˆo 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.

참고문헌 (14)

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  14. "An analogue of Wiener measure and its applications", 39, pp.801~819 (2002)

관련 논문AI추천

An analogue of Wiener measure and its applications류근식, 임만규대한수학회 · 대한수학회지2002 · 제39권 제5호Generalized Brownian motions with application to finance이정현, 정동명대한수학회 · 대한수학회지2006 · 제43권 제2호The Transformation Theorem on Analogue of Wiener Space임만규한국수학교육학회 · 이론수학과 교직수학2007 · 제14권 제4호Change of scale formulas for Wiener integral over paths in abstract Wiener space김병수, 김태수대한수학회 · 대한수학회논문집2006 · 제21권 제1호A Change of scale formula for conditional Wiener integrals on classical Wiener space유일, 김병수, 송택섭, 장건수, 조동현대한수학회 · 대한수학회지2007 · 제44권 제4호Conditional first variation over Wiener paths in abstract Wiener space조동현대한수학회 · 대한수학회지2005 · 제42권 제5호

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