Weak well-posedness of stochastic Volterra equations with completely monotone kernels and non-degenerate noise

Abstract

We establish weak existence and uniqueness in law for stochastic Volterra equations (SVEs for short) with completely monotone kernels and non-degenerate noise under mild regularity assumptions. In particular, our results reveal the regularization-by-noise effect for SVEs with singular kernels, allowing for multiplicative noise with Hölder diffusion coefficients. In order to prove our results, we reformulate the SVE into an equivalent stochastic evolution equation (SEE for short) defined on a Gelfand triplet of Hilbert spaces. We prove weak well-posedness of the SEE using stochastic control arguments, and then translate it into the original SVE.

36 pages

References in corpus (4)

• Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
• Uniqueness for Volterra-type stochastic integral equations
• Fluctuation limits for mean-field interacting nonlinear Hawkes processes
• Markovian lifting and asymptotic log-Harnack inequality for stochastic Volterra integral equations

Cited by in corpus (1)

• Small-time central limit theorems for stochastic Volterra integral equations and their Markovian lifts