On maximal inequalities for purely discontinuous martingales in infinite dimensions

2013/08/12 by Carlo Marinelli, Michael Röckner, Marinelli, Carlo +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.1308.2648

19 pages, no figures

arxiv created 2013/08/12 · openalex publication_date 2013/08/12 · arxiv updated 2013/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Local well-posedness of Musiela's SPDE with Lévy noise

Cited by

• Lyapunov exponents and growth indices for fractional stochastic heat equations with space-time Lévy white noise
• Ergodicity of conditional McKean-Vlasov jump diffusions
• On maximal inequalities for purely discontinuous L_q-valued martingales

Related

• On maximal inequalities for purely discontinuous L_q-valued martingales
• On the maximal inequalities of Burkholder, Davis and Gundy
• Maximal Inequalities and Some Applications
• From a stochastic maximal inequality to infinite-dimensional martingales
• Moderate and L^p maximal inequalities for diffusion processes and conformal martingales