Integration with respect to analogue of Wiener measure over paths in abstract Wiener space and its applications
Bull. Korean Math. Soc. 2010 Vol. 47, No. 1, 131-149
https://doi.org/10.4134/BKMS.2010.47.1.131
Printed January 1, 2010
Kun Sik Ryu
Han Nam University
Abstract : In 1992, the author introduced the definition and the properties of Wiener measure over paths in abstract Wiener space and this measure was investigated extensively by some mathematicians. In 2002, the author and Dr. Im presented an article for analogue of Wiener measure and its applications which is the generalized theory of Wiener measure theory. In this note, we will derive the analogue of Wiener measure over paths in abstract Wiener space and establish two integration formulae, one is similar to the Wiener integration formula and another is similar to simple formula for conditional Wiener integral. Furthermore, we will give some examples for our formulae.
Keywords : analogue of Wiener measure, measure-valued measure, Bartle integral, Bochner integral, stochastically independent, conditional expectation
MSC numbers : Primary 28C20; Secondary 28C35
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