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

2017/06/05 by C. A. Fonseca-Mora
Mathematics · #math.PR #msc:60H05 #msc:60H15 #msc:60B11 #msc:60G20 #msc:60G51

paper · pdf · doi:10.1007/s40072-018-0117-x

published as Stoch PDE: Anal Comp, 6, no.4, 618-689 (2018)

arxiv created 2017/06/05 · arxiv updated 2019/02/12

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.

Cited by

• Itô's formula for Lévy-Itô processes taking values in the dual of nuclear space