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Kalinin, Alexander (2021): Support characterization for regular path-dependent stochastic Volterra integral equations. In: Electronic Journal of Probability, Vol. 26, 29

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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 Holder continuous paths. Based on functional Ito calculus, we prove that the support of its law in Holder 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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