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Room P3.10, Mathematics Building

Gerardo Barrera Vargas, University of Helsinki, Finland

A coupling approach to quantify the transportation Wasserstein path-distance between heat equation and the Goldstein–Kac telegraph equation

In this talk, I will present a nonasymptotic process level control between the so-called telegraph process (a.k.a. Goldstein–Kac equation) and a diffusion process with suitable (explicit) diffusivity constant via a transportation Wasserstein path-distance with quadratic average cost.

We stress that the telegraph process solves a partial linear differential equation of the hyperbolic type for which explicit computations can be carried by in terms of Bessel functions. In the present talk, I will discuss a coupling approach, which is a robust technique that in principle can be used for more general PDEs. The proof is done via the interplay of the following couplings: coin-flip coupling, synchronous coupling and the celebrated Komlós–Major–Tusnády coupling. In addition, nonasymptotic estimates for the corresponding $L^p$ time average are given explicitly.

The talk is based on joint work with Jani Lukkarinen, University of Helsinki, Finland.