Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 2, Pages 105-111
doi:10.1155/S1048953399000118
Transformations of index set for Skorokhod integral with respect to Gaussian processes
Kettering University, (Formerly GMI Engineering and Management Institute), Department of Science and Mathematics, 1700 West Third Avenue, Flint 48504, MI, USA
Received 1 October 1997; Revised 1 December 1998
Copyright © 1999 Leszek Gawarecki. 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
We consider a Gaussian process {Xt,t∈T} with an arbitrary index set T
and study consequences of transformations of the index set on the Skorokhod integral and Skorokhod derivative with respect to X. The results applied to Skorokhod SDEs of diffusion type provide uniqueness of the solution
for the time-reversed equation and, to Ogawa line integral, give an analogue of the fundamental theorem of calculus.