The behavior of conditional Wiener integrals on product Wiener space. Issue 11 (27th March 2013)

• Record Type: Journal Article
• Authors: Choi, Jae Gil; Skouge, David; Chang, Seung Jun
• Is Part Of: Mathematische Nachrichten. Volume 286:Issue 11/12(2013)
• Page Start: 1114
• Page End: 1128
• Publication Date: 2013-03-27
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201200221
• Languages: English
• ISSNs: 0025-584X

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>In this paper we first investigate the behavior of conditional Wiener integrals on product Wiener spaces and then proceed to establish a Fubini theorem for conditional Wiener integrals. We then define a very general multiple conditional analytic Fourier‐Feynman transform and a multiple conditional analytic convolution product for functionals on Wiener space and then establish a relationship between them. Next we obtain a basic formula for the conditional Wiener integral involving the first variation and the <italic>n</italic>‐dimensional Wiener directional derivative. Finally we establish several evaluation formulas for conditional Wiener and Feynman integrals involving the <italic>n</italic>‐dimensional Wiener directional derivative of functionals on Wiener space.</p> </abstract>