Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 1, Pages 43-58
doi:10.1155/S1048953398000045
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.