Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 1, Pages 43-58
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.
In this paper, we propose a generalization of continuous-time processed
to the case of being a distribution. We give a necessary and sufficient
condition for , 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.