Markovian lifting and asymptotic log-Harnack inequality for stochastic Volterra integral equations

Speaker: Yushi Hamaguchi
Affiliation: Osaka University, Japan

Abstract

Solutions of stochastic Volterra integral equations (SVIEs) are neither Markovian nor semimartingales, and thus the usual It\^{o}'s calculus cannot be applied to SVIEs directly. In this talk, we introduce a new framework of Markovian lifts of SVIEs and show that the solution of an SVIE is represented by the solution of a lifted stochastic evolution equation (SEE) defined on a Hilbert space. Our framework can be a useful tool to study SVIEs by means of It\^{o}'s stochastic calculus in Hilbert spaces. Furthermore, we establish an asymptotic log-Harnack inequality for the Markov semigroup associated with the lifted SEE and show some important consequent properties including the uniqueness of the invariant probability measure for the lifted SEE.