Properties of stochastic integro-differential equations with infinite delay: Regularity, ergodicity, weak sense Fokker–Planck equations

This work focuses on properties of stochastic integro-differential equations with infinite delay (or unbounded delay). Our main approach is to map the solution processes into another Polish space. Under suitable conditions, it is shown that the resulting processes are Markov. Furthermore, sufficient conditions for Feller properties, recurrence, ergodicity, and existence of invariant measures are obtained. Moreover, weak sense Fokker–Planck equations are derived for the underlying processes.