|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
q-Wiener and related processes. A continuous time generalization of Bryc processes | | Pawe{l} J. Szab{l}owski
; | | Date: |
14 Jul 2005 | | Subject: | Probability MSC-class: Primary 60J25, 60G44; Secondary 05A30, 60K40 | math.PR | | Abstract: | We define two Markov processes. The finite dimensional distributions of the first one (say $mathbf{X=}(X_{t})_{tgeq0})$ depend on one parameter $qin(-1,1>$ and of the second one (say $mathbf{Y=}(Y_{t})_{tinmathbb{R}})$ on two parameters $(q,alpha) in(-1,1> imes(0,infty).$ The first one resembles Wiener process in the sense that for $q=1$ it is Wiener process but also that for $q<1$ and $forall ngeq1$ $t^{n/2}H_{n}(X_{t}/sqrt{t}|q) ,$ where $(H_{n})_{ngeq0}$ are so called $q-$Hermite polynomials, are martingales. It does not have however independent increments. The second one resembles Orstein-Ulehnbeck processes. For $q=1$ it is a classical OU process. For $q<1$ it is stationary with correlation function equal to $exp (-alpha|t-s|).$When defining these processes and proving their existence we use properties of discrete time Bryc processes and solve the problem of their existence for $q>1.$ On the way we deny Wesolowski’s martingale characterization of Wiener process. | | Source: | arXiv, math.PR/0507303 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER