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

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Publication details

JournalSIAM journal on mathematical analysis
DateAccepted/In press - 6 Mar 2019
DateE-pub ahead of print (current) - 23 May 2019
Number of pages47
Pages (from-to)2121–2167
Early online date23/05/19
Original languageEnglish


We present remarkably simple proofs of Burkholder–Davis–Gundy inequalities for
stochastic integrals and maximal inequalities for stochastic convolutions in Banach spaces driven by Levy-type processes. Exponential estimates for stochastic convolutions are obtained and two versions
of Ito’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 Levy noise is established.

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    Research areas

  • Burkholder–Davis–Gundy inequality, maximal inequality, exponential estimate, stochastic convolution, Itˆo formula, martingale type r Banach space

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