Support characterization for regular path-dependent stochastic Volterra integral equations

Abstract

We consider a stochastic Volterra integral equation with regular path-dependent coefficients and a Brownian motion as integrator in a multidimensional setting. Under an imposed absolute continuity condition, the unique solution is a semimartingale that admits almost surely Hölder continuous paths. Based on functional Itô calculus, we prove that the support of its law in the Hölder norm can be described by a flow of mild solutions to ordinary integro-differential equations that are constructed by means of the vertical derivative of the diffusion coefficient.

References in corpus (1)

• On the support of solutions of stochastic differential equations with path-dependent coefficients

Cited by in corpus (1)

• Time-inconsistency with rough volatility