Long-time behaviour and regularity properties of transition semigroups of Fleming–Viot processes

Abstract

Let A be a Feller generator on a compact space and L be the corresponding Fleming–Viot (FV) operator with no selection and no recombination. In this paper we give conditions on A implying that the semigroup (T t ) generated by L (i) converges towards equilibrium with exponential rate (moreover, we determine explicit bounds on the rate of convergence in terms of A), (ii) is hypercontractive, (iii) is strong Feller, and (iv) is compact. We give applications of the last result to the existence of invariant measures for FV-operators with interactive selection.