文章基本信息

标题：A Conditional Fourier-Feynman Transform and Conditional Convolution Product with Change of Scales on a Function Space II
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作者：Dong Hyun Cho
期刊名称：Journal of Probability and Statistics
印刷版ISSN：1687-952X
电子版ISSN：1687-9538
出版年度：2017
卷号：2017
DOI：10.1155/2017/8510782
出版社：Hindawi Publishing Corporation
摘要：Using a simple formula for conditional expectations over continuous paths, we will evaluate conditional expectations which are types of analytic conditional Fourier-Feynman transforms and conditional convolution products of generalized cylinder functions and the functions in a Banach algebra which is the space of generalized Fourier transforms of the measures on the Borel class of . We will then investigate their relationships. Particularly, we prove that the conditional transform of the conditional convolution product can be expressed by the product of the conditional transforms of each function. Finally we will establish change of scale formulas for the conditional transforms and the conditional convolution products. In these evaluation formulas and change of scale formulas, we use multivariate normal distributions so that the conditioning function does not contain present positions of the paths.