International Journal of Stochastic Analysis

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International Journal of Stochastic Analysis / 1998 / Article

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Volume 11 |Article ID 823585 | 16 pages | https://doi.org/10.1155/S1048953398000045

Linear distribution processes

L. Bel,1 G. Oppenheim,1 L. Robbiano,1 and M. C. Viano1

1Equipe de modélisation, stochastique et statistique, Bât 425, Université de Paris Sud, France

Received01 May 1996
Revised01 Jun 1997

Abstract

In this paper, we propose a generalization of continuous-time processed defined by Xt=∫f(t−s)dWs, to the case of f being a distribution. We give a necessary and sufficient condition for f, such that the obtained process is a second order distribution process. We study the moments and the regularity of these processes. In addition, we investigate a generalization to processes with stationary increments.

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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