Sticky-Schrödinger problem: from Large Deviation principle to JKO scheme

Nenna Luca, Université Paris-Saclay

In this talk we consider the Sticky-Schrödinger problem, namely the minimisation of a relative entropy with respect to the sticky Brownian motion under marginal constraints. Roughly speaking the sticky brownian process is a stochastic process which behaves as a standard diffusions in the interior of the prescribed domain and when it hints the boundary it sticks following an intrinsic tangential diffusion. We carefully derive a large variation principle and identify the limit functional which turns out to be an Optimal Transport problem (OT) with a given cost $d_\nu$ , where $\nu$ is the tangential viscosity. Moreover this OT problem defines a distance between probability measures and in the special case of $d_{\infty}$ we study the associated JKO scheme. This talk is based on joint works with Jean-Baptiste Casteras and Léonard Monsaigeon.

Area: CS34 - Advances in stochastic optimal transport and applications (Luca Tamanini)

Keywords: Optimal Transport, Sticky Brownian, Schrödinger

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