Support characterization for regular path-dependent stochastic Volterra integral equations
Probability
2021-03-29 v1
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 H\"older continuous paths. Based on functional It\^o calculus, we prove that the support of its law in the H\"older 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.
Cite
@article{arxiv.1908.10786,
title = {Support characterization for regular path-dependent stochastic Volterra integral equations},
author = {Alexander Kalinin},
journal= {arXiv preprint arXiv:1908.10786},
year = {2021}
}