Support characterization for regular path-dependent stochastic Volterra integral equations

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

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 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1083-6489
• Language: English