Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 1, Pages 43-58
doi:10.1155/S1048953398000045
Linear distribution processes
Equipe de modélisation, stochastique et statistique, Bât 425, Université de Paris Sud, Orsay Cedex 91 405, France
Received 1 May 1996; Revised 1 June 1997
Copyright © 1998 L. Bel et al. 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.
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.