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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Liu, Xuan¹  Xi, Guangyu² 

[1] Normura Int, 30 FL Two Int Finance Ctr, Hong Kong, Peoples R China

[2] Univ Maryland, Dept Math, College Pk, MD 20742 USA

关键词: Doob's maximal inequality;    Kolmogorov's criteria;    Divergence-free;    Aronson estimate;   

DOI  :  10.1016/j.spa.2019.12.004

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free