4 papers · 1 filter
A Route to Harris ergodicity for Non-Feller Markov Kernels
Jean-Gabriel Attali
For non-Feller Markov kernels satisfying a quasi-Feller factorization, the compact-petite-set criterion gives petite compact sets under \(ψ\)-irreducibility when the support of \(ψ…
Equilibrium Biphasicity and Non-Binary Pathwise Confinement in Stochastic Ising Models
Jean-Gabriel Attali
For the low-temperature two-dimensional Ising model, the two pure Gibbs phases exhaust the extremal equilibrium states, but not the pathwise absorbing structure of the Glauber dyna…
Existence and uniqueness of invariant measures for non-Feller Markov semigroups
Jean-Gabriel Attali
We study existence and uniqueness of invariant probability measures for continuous-time Markov processes on general state spaces. Existence is obtained from tightness of time avera…
Asymptotic Stability and Equilibrium Selection in Quasi-Feller Systems with Minimal Moment Conditions
Jean-Gabriel Attali
We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general q…