Functional inequalities for forward and backward diffusions

Daniel Bartl, Ludovic Tangpi

Research output: Contribution to journalArticle

Abstract

In this article we derive Talagrand’s T2 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.

Original languageEnglish (US)
Article number94
Pages (from-to)1-22
Number of pages22
JournalElectronic Journal of Probability
Volume25
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Backward stochastic differential equation
  • Concentration of measures
  • Logarithmic-Sobolev inequality
  • Non-smooth coefficients
  • Optimal stopping
  • Quadratic transportation inequality
  • Stochastic differential equation

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