Stochastic Integration and Stochastic PDEs Driven by Jumps on the Dual of a Nuclear Space

Abstract

We develop a novel theory of weak and strong stochastic integration for cylindrical martingale-valued measures taking values in the dual of a nuclear space. This is applied to develop a theory of SPDEs with rather general coefficients. In particular, we can then study SPDEs driven by general Lévy processes in this context.

References in corpus (1)

• Existence of Continuous and Càdlàg Versions for Cylindrical Processes in the Dual of a Nuclear Space

Cited by in corpus (11)

• Lévy Processes and Infinitely Divisible Measures in the Dual of a Nuclear Space
• Stochastic integration in Hilbert spaces with respect to cylindrical martingale-valued measures
• Semimartingales on Duals of Nuclear Spaces
• Stochastic Evolution Equations with Lévy Noise in the Dual of a Nuclear Space
• Stochastic integration with respect to cylindrical semimartingales
• Regularization of Cylindrical Processes In Locally Convex Spaces
• Convergence Uniform on Compacts in Probability with Applications to Stochastic Analysis in Duals of Nuclear Spaces
• Time regularity of stochastic convolutions and stochastic evolution equations in duals of nuclear spaces
• Almost Sure Uniform Convergence of Stochastic Processes in the Dual of a Nuclear Space
• Cylindrical Martingale-Valued Measures, Stochastic Integration and SPDEs
• Tightness and weak convergence in the topology of local uniform convergence for stochastic processes in the dual of a nuclear space