Some refinements of existence results for SPDEs driven by Wiener processes and Poisson random measures

Abstract

We provide existence and uniqueness of global (and local) mild solutions for a general class of semilinear stochastic partial differential equations driven by Wiener processes and Poisson random measures under local Lipschitz and linear growth (or local boundedness, resp.) conditions. The so-called "method of the moving frame" allows us to reduce the SPDE problems to SDE problems.

18 pages

Cited by in corpus (5)

• The Yamada-Watanabe Theorem for mild solutions to stochastic partial differential equations
• Invariance of closed convex cones for stochastic partial differential equations
• Mild solutions to semilinear stochastic partial differential equations with locally monotone coefficients
• The dual Yamada-Watanabe theorem for mild solutions to stochastic partial differential equations
• Foundations of the theory of semilinear stochastic partial differential equations