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 Hölder norms 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.
The author is grateful for the support from Imperial College London by a Chapman fellowship.
"Support characterization for regular path-dependent stochastic Volterra integral equations." Electron. J. Probab. 26 1 - 29, 2021. https://doi.org/10.1214/20-EJP576