Stochastic Evolution Equations with Multiplicative Poisson Noise and Monotone Nonlinearity: A New Approach

Abstract

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and uniqueness of the mild solution is proposed. Examples on stochastic partial differential equations and stochastic delay differential equations are provided to demonstrate the theory developed.

arXiv admin note: substantial text overlap with arXiv:1304.2122

Cited by in corpus (1)

• Well-posedness for Stochastic Evolution Equations with Monotone Non-linearity and Multiplicative Poisson Noise in $L^p$