Characterization of a wiener process taking values in a Hilbert space
Department Of Mathematics, Saradha Gangadharan College, Puducherry – 605010, India.
Review Article
World Journal of Advanced Research and Reviews, 2024, 24(01), 2379–2385
Publication history:
Received on 08 September 2024; revised on 15 October 2024; accepted on 18 October 2024
Abstract:
This paper characterize wiener process by taking values in a Hilbert space.
A standard wiener process is stochastic process {Wt }t≥0+ indesed by nonnegative real numbers t with the following properties:
W0 = 0
With probability 1, the function t → Wt is continuous in t.
The process {Wt }t≥0 has stationary, independent increments.
The increments Wt+s- Ws has the NORMAL (0,t) distribution
Keywords:
Wiener process; Hilbert space; Characteristic function; Orthonormal system.
Full text article in PDF:
Copyright information:
Copyright © 2024 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0