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- Title
Stochastic PDEs in đŽ' for SDEs driven by LÊvy noise.
- Authors
Bhar, Suprio; Bhaskaran, Rajeev; Sarkar, Barun
- Abstract
In this article we show that a finite-dimensional stochastic differential equation driven by a LÊvy noise can be formulated as a stochastic partial differential equation (SPDE) driven by the same LÊvy 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.
- Subjects
STOCHASTIC partial differential equations; STOCHASTIC differential equations; FORTRAN; NOISE
- Publication
Random Operators & Stochastic Equations, 2020, Vol 28, Issue 3, p217
- ISSN
0926-6364
- Publication type
Article
- DOI
10.1515/rose-2020-2041