On a maximal inequality and its application to SDEs with singular drift

Xuan Liu and Guangyu Xi

Stochastic Processes and their Applications, 2020, vol. 130, issue 7, 4275-4293

Abstract: In this paper we present a Doob type maximal inequality for stochastic processes satisfying the conditional increment control condition. If we assume, in addition, that the margins of the process have uniform exponential tail decay, we prove that the supremum of the process decays exponentially in the same manner. Then we apply this result to the construction of the almost everywhere stochastic flow to stochastic differential equations with singular time dependent divergence-free drift.

Keywords: Doob’s maximal inequality; Kolmogorov’s criteria; Divergence-free; Aronson estimate (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.12.004

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