Bernat Bassols Cornudella

Conditioned Stochastic Stability of Equilibrium States on Repellers

Stochastic stability provides a framework to identify relevant invariant measures in a dynamical system in the sense that they persist under random perturbations of the dynamics. Adding noise to a system washes out any invariant repelling sets and smears all points towards an attracting region of the state space. Consequently, stochastic stability has only been studied for measures on attractors. In this talk, we introduce the notion of conditioned stochastic stability of invariant measures on repellers: we consider whether quasi-ergodic measures of absorbing Markov processes, generated by random perturbations of the deterministic dynamics and conditioned upon survival in a neighbourhood of a repeller, converge to an invariant measure in the zero-noise limit.

This is joint work with Matheus M de Castro (UNSW) and Jeroen S.W. Lamb (Imperial College London).