Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050
Special Issue: New Trends in Infinite Dimensional Analysis and Quantum Probability
Survey of the Theories for Analogue of Wiener Measure Space
Kun Sik RYUMan Kyu IMKi Seong CHOI
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JOURNAL FREE ACCESS

2009 Volume 15 Issue 3 Pages 319-337

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Abstract

We consider the analogue of Wiener measure on the space of all real continuous functions, and then establish the measure-valued measure and the operator-valued measure on our space and we investigate their important properties, for example, the integration formula, the rotation theorem, the Bartle integral, the Bochner integral and the Dobrakov integral, the simple formula for conditional expectation, the measure-valued Feynman-Kac formula and Volterra integral equation and integral transform.

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© 2009 by the Graduate School of Information Sciences (GSIS), Tohoku University

This article is licensed under a Creative Commons [Attribution 4.0 International] license.
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