Singular integrals of subordinators with applications to structural properties of SPDEs

2020/09/10 by Chang‐Song Deng, Deng, Changsong, René L. Schilling +3 · 1 citation
Economics, Econometrics and Finance · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2009.04785

openalex publication_date 2020/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study stochastic integrals driven by a general subordinator and establish a zero-one law for the finiteness of the resulting integral as well as moment estimates. As an application, we use these results to obtain structural properties of SPDEs driven by multiplicative pure jump noise, which include (1) a maximal inequality for a multiplicative stochastic convolution Z_t, (2) a small ball probability of Z_t, (3) the existence of invariant measures and accessibility to zero of SPDEs, and (4) a Galerkin approximation of solutions to SPDEs.

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• Weak irreducibility of stochastic delay differential equation driven by pure jump noise

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