A conditional Fourier-Feynman transform and conditional convolution product with change of scales on a function space. II
type: Item
instance of: scholarly article
title: A conditional Fourier-Feynman transform and conditional convolution product with change of scales on a function space. II
zbMATH Open document ID: 1431.43002
DOI: 10.1155/2017/8510782
author: Dong Hyun Cho
published in: Journal of Probability and Statistics
publication date: 2018-08-14T00:00:00Z
review text: Summary: 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 \(L_2 [0, T]\). 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. For Part I, see [the author, Bull. Korean Math. Soc. 54, No. 2, 687--704 (2017; Zbl 1388.43003)].
Mathematics Subject Classification ID: 43A25
Mathematics Subject Classification ID: 28C20
zbMATH DE Number: 6917560
Wikidata QID: Q59147021
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/8510782
OpenAlex ID: W2593443602
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description: scientific article; zbMATH DE number 6917560