Stochastic PDEs in $\mathcal{S}^\prime$ for SDEs driven by L\'evy noise
Probability
2018-02-15 v2
Abstract
In this article we show that a finite dimensional stochastic differential equation driven by a L\'evy process can be formulated as a stochastic partial differential equation. We prove the existence and uniqueness of strong solutions of such stochastic PDEs. The solutions that we construct have the `translation invariance' property. The special case of this correspondence for diffusion processes was proved in [Rajeev, Translation invariant diffusion in the space of tempered distributions, Indian J. Pure Appl. Math. 44 (2013), no.~2, 231--258].
Keywords
Cite
@article{arxiv.1801.06772,
title = {Stochastic PDEs in $\mathcal{S}^\prime$ for SDEs driven by L\'evy noise},
author = {Suprio Bhar and Rajeev Bhaskaran and Barun Sarkar},
journal= {arXiv preprint arXiv:1801.06772},
year = {2018}
}