On Classical Solutions of Linear Stochastic Integro-Differential Equations
Abstract
We prove the existence of classical solutions to parabolic linear stochastic integro-differential equations with adapted coefficients using Feynman-Kac transformations, conditioning, and the interlacing of space-inverses of stochastic flows associated with the equations. The equations are forward and the derivation of existence does not use the "general theory" of SPDEs. Uniqueness is proved in the class of classical solutions with polynomial growth.
Keywords
Cite
@article{arxiv.1404.0345,
title = {On Classical Solutions of Linear Stochastic Integro-Differential Equations},
author = {James-Michael Leahy and Remigijus Mikulevicius},
journal= {arXiv preprint arXiv:1404.0345},
year = {2014}
}
Comments
50 pages; We have removed some of the material on inverse flows and moved it to the paper "On Some Properties of Space Inverses of Stochastic Flows" (arXiv:1411.6277). Also, the assumptions for our main existence theorem (Theorem 2.5 in new version) have been modified and we have formulated our representation theorem (Theorem 2.2 in new version) for an equation with a special form