Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 130940, 17 pages
Fredholm Determinant of an Integral Operator Driven by a Diffusion Process
Department of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nashville, TN 37240, USA
Received 10 May 2008; Accepted 9 September 2008
Academic Editor: Hong Kun Xu
Copyright © 2008 Adrian P. C. Lim. 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.
This article aims to give a formula for differentiating, with respect to , an expression of the form , where and is a diffusion process starting from , taking values in a manifold, and the expectation is taken with respect to the law of this process. is a trace class operator defined by , where , are locally Lipschitz, positive matrices.