Section: New Results

Asymptotic variance reduction

Participant : Mathias Rousset.

Recently, M. Rousset has initiated a research topic on variance reduction techniques (called ”asymptotic”) for the simulation of stochastic models of particles. The point is to use a macroscopic (or model reduced) equation as a control variate; or in other words, to use the information of a macroscopic description to decrease the statistical error of the simulated microscopic evolution.

A first step in this program has been achieved for a microscopic model describing the individual motion of bacteriae with a Markovian velocity-jump process. The macroscopic equation is an advection-diffusion equation called the chemotaxis equation. In [44] , the pobabilistic derivation of the chemotaxis equation from the individual motion of bacteriae have been carried out in a rigorous way. In [45] , a numerical method simulating the individual evolution of bacteriae with ”asymptotic” variance reduction have been proposed.