Séminaire Orléans

Stationary states for stable processes with partial resetting

by Bartosz Trojan (Académie des Sciences de Pologne)

Salle de Séminaires (Orléans)

Salle de Séminaires



We consider a d-dimensional stochastic process X which develops from a Lévy process Y by partial resetting at Poisson epochs. The partial resetting means that at Poisson moments we reposition the process X to a point which is a multiple by a factor c ∈ (0,1) of the position right before this moment. In this talk we mainly focus on the case of Brownian motion for which we discuss the existence of non-equilibrium stationary states (NESS), that is a phenomenon of a phase transition that corresponds to the change of the asymptotic behavior of the density p(t; x, y) of the process X started at x with regard to the time-space regime (y, t) as t tends to infinity. The talk is based on the joint work with Tomasz Grzywny, Zbigniew Palmowski and Karol Szczypkowski.