Optimal Couplings on Wiener Space and An Extension of Talagrand’s Transport Inequality

Hans Föllmer ()
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Hans Föllmer: Humboldt-Universität zu Berlin, Institut fùr Mathematik, Unter den Linden 6, 10099

A chapter in Stochastic Analysis, Filtering, and Stochastic Optimization, 2022, pp 147-175 from Springer

Abstract: Abstract For a probability measure Q on Wiener space, Talagrand’s transport inequality takes the formWϰ (Q,P)2 ≤2H(Q|P), where theWasserstein distanceWϰ is defined in terms of the Cameron-Martin norm, and where H(Q|P) denotes the relative entropy with respect to Wiener measure P. Talagrand’s original proof takes a bottom-up approach, using finite-dimensional approximations. As shown by Feyel and Üstünel in [3] and Lehec in [10], the inequality can also be proved directly on Wiener space, using a suitable coupling of Q and P. We show how this top-down approach can be extended beyond the absolutely continuous case Q

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-98519-6_7

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DOI: 10.1007/978-3-030-98519-6_7

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