A Conditional Fourier-Feynman Transform and Conditional Convolution Product with Change of Scales on a Function Space II
Author
Source
Journal of Probability and Statistics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-02-28
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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 L2[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.
American Psychological Association (APA)
Cho, Dong Hyun. 2017. A Conditional Fourier-Feynman Transform and Conditional Convolution Product with Change of Scales on a Function Space II. Journal of Probability and Statistics،Vol. 2017, no. 2017, pp.1-13.
https://search.emarefa.net/detail/BIM-1186293
Modern Language Association (MLA)
Cho, Dong Hyun. A Conditional Fourier-Feynman Transform and Conditional Convolution Product with Change of Scales on a Function Space II. Journal of Probability and Statistics No. 2017 (2017), pp.1-13.
https://search.emarefa.net/detail/BIM-1186293
American Medical Association (AMA)
Cho, Dong Hyun. A Conditional Fourier-Feynman Transform and Conditional Convolution Product with Change of Scales on a Function Space II. Journal of Probability and Statistics. 2017. Vol. 2017, no. 2017, pp.1-13.
https://search.emarefa.net/detail/BIM-1186293
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1186293