**Financial support through the following projects:**

UID/MAT/00297/2019

UID/MAT/00297/2013

PEst-OE/MAT/UI0297/2014

PEst-OE/MAT/UI0297/2011

Título: **Bernstein processes, parabolic problems and spectral theory**

by Pierre A. Vuillermot , University of Lisbon and IECL, Nancy, France

Data: 17/10/2018

Hora: 14h00

Local: Sala 1.4 - Edifício VII, FCT-UNL

**Abstract: **Bernstein processes, also named Schrödinger or reciprocal processes in the literature, constitute a generalization of Markov processes and have played an increasingly important rôle in Mathematics and Mathematical physics over the years, particularly in view of the recent advances in the Monge-Kantorovitch formulation of Optimal Transport Theory and Stochastic Geometric Mechanics. In this talk I will show how to construct such processes from an infinite hierarchy of forward-backward systems of linear deterministic parabolic partial differential equations, when the elliptic part of the parabolic operators may be realized as an unbounded Schrödinger operator with compact resolvent in standard L2-space. I will also discuss many important properties of such processes, including those of a natural entropy function associated with them. This is joint work with J. C. Zambrini.