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

Xuan Liu; Guangyu Xi

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arXiv · 1905.13286

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

Xuan Liu·Guangyu Xi

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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.

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Xuan Liu, Guangyu Xi. 2019-05-30. On a maximal inequality and its application to SDEs with singular drift. https://arxiv.org/abs/1905.13286

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