Functional inequalities for forward and backward diffusions
Functional inequalities for forward and backward diffusions
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DOI：
10.1214/20-ejp495
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发表时间：
2019-10
影响因子：
1.4
通讯作者：
Daniel Bartl;Ludovic Tangpi
中科院分区：
文献类型：
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作者：
Daniel Bartl;Ludovic Tangpi
在本文中，我们推导出路径空间上的 Talagrand 的 $T_2$ 不等式。各种随机过程的最大范数，包括具有可测量漂移的一维随机微分方程的解、后向随机微分方程以及最优停止问题的值过程。证明没有使用吉尔萨诺夫方法，而是使用路径论证。这些用于表明我们感兴趣的所有过程都是已知满足所需函数不等式的过程的 Lipschitz 变换。
In this article we derive Talagrand's $T_2$ inequality on the path space w.r.t. the maximum norm for various stochastic processes, including solutions of one-dimensional stochastic differential equations with measurable drifts, backward stochastic differential equations, and the value process of optimal stopping problems. The proofs do not make use of the Girsanov method, but of pathwise arguments. These are used to show that all our processes of interest are Lipschitz transformations of processes which are known to satisfy desired functional inequalities.