Maximal inequalities and exponential estimates for stochastic convolutions driven by Lévy-type processes in Banach spaces with application to stochastic quasi-geostrophic equations

Abstract

We present remarkably simple proofs of Burkholder-Davis-Gundy inequalities for stochastic integrals and maximal inequalities for stochastic convolutions in Banach spaces driven by Lévy-type processes. Exponential estimates for stochastic convolutions are obtained and two versions of Itô's formula in Banach spaces are also derived. Based on the obtained maximal inequality, the existence and uniqueness of mild solutions of stochastic quasi-geostrophic equation with Lévy noise is established.

arXiv comment39 pages

References in corpus (4)

• Ten equivalent definitions of the fractional Laplace operator
• Sub and supercritical stochastic quasi-geostrophic equation
• Large deviation principles for the stochastic quasi-geostrophic equation
• Itô isomorphisms for $L^p$-valued Poisson stochastic integrals

Cited by in corpus (4)

• Maximal estimates for stochastic convolutions in 2-smooth Banach spaces and applications to stochastic evolution equations
• The Stochastic Strichartz estimates and stochastic nonlinear Schrödinger equations driven by Lévy noise
• Maximal inequalities for stochastic convolutions and pathwise uniform convergence of time discretisation schemes
• Stochastic Evolution Equations with Lévy Noise in the Dual of a Nuclear Space