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, Bd. 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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik ; Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1083-6489
• Sprache: Englisch