Wednesday, February 13, 2019

How to obtain deterministic laws from a random motion of particles

Patrícia Gonçalves
(Instituto Superior Técnico)

Abstract: I am going to describe a way to derive rigorously the laws that rule the space-time evolution of the conserved quantities of a certain stochastic process. The goal is to describe the connection between the macroscopic equations and the microscopic system of random particles. The former can be either PDEs or stochastic PDEs depending on whether one is looking at the law of large numbers or the central limit theorem; while the later is a collection of particles that move randomly according to some transition probability that one can choose. Depending on this choice, we will see that the macroscopic laws can be of different nature. I will present a model for which we can obtain a fractional reaction-diffusion equation given in terms of the regional fractional Laplacian.

Wednesday, February 13, 2019
Time: 14h00
Room: Sala Delta, Edificio Quelhas, ISEG