A simple formula for an analogue of conditional Wiener integrals and its applications

Author:
Dong Hyun Cho

Journal:
Trans. Amer. Math. Soc. **360** (2008), 3795-3811

MSC (2000):
Primary 28C20

DOI:
https://doi.org/10.1090/S0002-9947-08-04380-8

Published electronically:
January 30, 2008

MathSciNet review:
2386246

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the space of real-valued continuous functions on the interval and for a partition of , let be given by .

In this paper, with the conditioning function , we derive a simple formula for conditional expectations of functions defined on which is a probability space and a generalization of Wiener space. As applications of the formula, we evaluate the conditional expectation of functions of the form

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Additional Information

**Dong Hyun Cho**

Affiliation:
Department of Mathematics, Kyonggi University, Kyonggido Suwon 443-760, Korea

Email:
j94385@kyonggi.ac.kr

DOI:
https://doi.org/10.1090/S0002-9947-08-04380-8

Keywords:
Analogue of Wiener measure,
conditional Cameron-Martin translation theorem,
conditional Wiener integral,
simple formula for conditional $w_\varphi$-integral

Received by editor(s):
May 30, 2006

Published electronically:
January 30, 2008

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.