On entropy functionals associated with Bernstein stochastic processes
 
 
Description:  Bernstein processes constitute a generalization of Markov processes, and there are many equivalent ways to define them. In this talk I will show how to generate such processes from a hierarchy of forward-backward systems of decoupled deterministic linear parabolic partial differential equations defined on open bounded domains of Euclidean space of arbitrary dimension, subject to Neumann boundary conditions. This will be done under the assumption that the elliptic part of the parabolic operator in the equations is a self-adjoint Schrödinger operator with compact resolvent in the usual L2-space. I will then proceed by displaying a class of statistical operators defined from sequences of probabilities associated with the pure point spectrum of the elliptic part in question, which will allow a preliminary classification of the processes we alluded to above. I will also introduce a class of entropy functionals for them and showin particular that the Bernstein processes of maximal von Neumann entropyare those for which the associated sequences of probabilities are of Gibbs type. I will finally illustrate some of theresults by considering processes associated with a specific hierarchy of forward-backward heat equations defined in a two-dimensional disk. If time permits, I will indicate in what sense Bernstein processes are related to Optimal Transport Theory.
Date:  2019-10-18
Start Time:   14:30
Speaker:  Pierre Viullermot (Univ. Lorraine & Univ. Lisboa)
Institution:  Univ. Lorraine & Univ. Lisboa
Place:  Sala 5.5
Research Groups: -Analysis
-Probability and Statistics
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