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 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.
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