Maximal inequalities and exponential estimates for stochastic convolutions driven by L\'evy-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 L\'evy-type processes. Exponential estimates for stochastic convolutions are obtained and two versions of It\o'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 L\'evy noise is established.
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