Stochastic PDEs in S' for SDEs driven by Lévy noise
Random Operators and Stochastic Equations
In this article we show that a finite-dimensional stochastic differential equation driven by a Lévy noise can be formulated as a stochastic partial differential equation (SPDE) driven by the same Lévy noise. We prove the existence result for such an SPDE by Itô’s formula for translation operators, and the uniqueness by an adapted form of “Monotonicity inequality”, proved earlier in the diffusion case. As a consequence, the solutions that we construct have the “translation invariance” property.
Bhar, Suprio; Bhaskaran, Rajeev; and Sarkar, Barun, "Stochastic PDEs in S' for SDEs driven by Lévy noise" (2020). Journal Articles. 140.