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arXiv · 1908.10786

Support characterization for regular path-dependent stochastic Volterra integral equations

Alexander Kalinin
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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.

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Alexander Kalinin. 2019-08-28. Support characterization for regular path-dependent stochastic Volterra integral equations. https://doi.org/10.1214/20-ejp576

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