James-Michael Leahy, Remigijus Mikulevicius
Published 2014-11-23Version 1
We derive moment estimates and a strong limit theorem for space inverses of stochastic flows generated by jump SDEs with adapted coefficients in weighted H\"older norms using the Sobolev embedding theorem and the change of variable formula. As an application of some basic properties of flows of continuous SDEs, we derive the existence and uniqueness of classical solutions of linear parabolic second order SPDEs by partitioning the time interval and passing to the limit. The methods we use allow us to improve on previously known results in the continuous case and to derive new ones in the jump case.
Comments: 30 pages; Part of the material of this paper is from the first version of our paper entitled "On Classical Solutions of Linear Stochastic Integro-Differential Equations" (arXiv:1404.0345). We have removed this material from arXiv:1404.0345
On a Class of Stochastic Differential Equations With Jumps and Its Properties
Properties of the density for a three dimensional stochastic wave equation
Properties of Expectations of Functions of Martingale Diffusions
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