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Stochastic calculus for analogue of Wiener process. (English) Zbl 1178.60028

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.

MSC:

60G15 Gaussian processes
60H05 Stochastic integrals
93E11 Filtering in stochastic control theory
60G35 Signal detection and filtering (aspects of stochastic processes)
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