On maximal inequalities for purely discontinuous martingales in infinite dimensions

Abstract

The purpose of this paper is to give a survey of a class of maximal inequalities for purely discontinuous martingales, as well as for stochastic integral and convolutions with respect to Poisson measures, in infinite dimensional spaces. Such maximal inequalities are important in the study of stochastic partial differential equations with noise of jump type.

19 pages, no figures

References in corpus (4)

• Itô isomorphisms for $L^p$-valued Poisson stochastic integrals
• Maximal inequality of Stochastic convolution driven by compensated Poisson random measures in Banach spaces
• On maximal inequalities for purely discontinuous $L_q$-valued martingales
• Local well-posedness of Musiela's SPDE with Lévy noise