A Conditional Fourier-Feynman Transform and Conditional Convolution Product with Change of Scales on a Function Space II. (28th February 2017)

• Record Type: Journal Article
• Authors: Cho, Dong Hyun
• Other Names: Rodríguez-Dagnino Ramón M. Academic Editor.
• Is Part Of: Journal of probability and statistics. Volume 2017(2017)
• Publication Date: 2017-02-28
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Periodicals; 519
• DOI: 10.1155/2017/8510782
• Languages: English
• ISSNs: 1687-952X

Abstract

Abstract : 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.