Lévy Flows and associated Stochastic PDEs

2022/06/28 by Nath, Arvind Kumar, Bhar, Suprio
#60G51 #60H10 #60H15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2206.14129

Abstract

In this paper, we first explore certain structural properties of Lévy flows and use this information to obtain the existence of strong solutions to a class of Stochastic PDEs in the space of tempered distributions, driven by Lévy noise. The uniqueness of the solutions follows from Monotonicity inequality. These results extend an earlier work Bhar (2017) on the diffusion case.

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• Parametric family of SDEs driven by Lévy noise
• Stochastic PDEs in S^′ for SDEs driven by Lévy noise
• Strong solutions for SPDE with locally monotone coefficients driven by Lévy noise
• Weak Solutions of SPDEs in the space of Tempered distributions
• Stochastic flows for Lévy processes with Hölder drifts