Groupe d’études et de recherche en analyse des décisions

An ergodic variant of the telegraph process for a toy model of bacterial chemotaxis

Hélène Guérin

I will study the long time behavior of a variant of the classic telegraph process, with non-constant jump rates that induce a drift towards the origin.. This process can be seen as a toy model for velocity-jump processes recently proposed as mathematical models of bacterial chemotaxis. I will give its invariant law and construct an explicit coupling for velocity and position, providing exponential ergodicity with moreover a quantitative control of the total variation distance to equilibrium at each time instant.

It is a joint work with Joaquin Fontbona (Universidad de Santiago, Chile) and Florent Malrieu (Université Rennes 1, France).