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Functional inequalities for forward and backward diffusions. (English) Zbl 1459.60156

Summary: 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.

MSC:

60J60 Diffusion processes
60G40 Stopping times; optimal stopping problems; gambling theory
60E15 Inequalities; stochastic orderings
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