Cylindrical Martingale-Valued Measures, Stochastic Integration and SPDEs

Abstract

We develop a theory of Hilbert-space valued stochastic integration with respect to cylindrical martingale-valued measures. As part of our construction, we expand the concept of quadratic variation, introduced by Veraar and Yaroslavtsev (2016), to the case of cylindrical martingale-valued measures that are allowed to have discontinuous paths (this is carried out within the context of separable Banach spaces). Our theory of stochastic integration is applied to address the existence and uniqueness of solutions to stochastic partial differential equations in Hilbert spaces.

This is an updated version with new examples and remarks

References in corpus (7)

• Cylindrical Levy processes in Banach spaces
• Itô isomorphisms for $L^p$-valued Poisson stochastic integrals
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• Stochastic Integration and Stochastic PDEs Driven by Jumps on the Dual of a Nuclear Space
• Time fractional stochastic differential equations driven by pure jump Lévy noise
• Stochastic integration in Hilbert spaces with respect to cylindrical martingale-valued measures