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2021 Support characterization for regular path-dependent stochastic Volterra integral equations
Alexander Kalinin
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Electron. J. Probab. 26: 1-29 (2021). DOI: 10.1214/20-EJP576


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 Hölder 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.


The author is grateful for the support from Imperial College London by a Chapman fellowship.


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Alexander Kalinin. "Support characterization for regular path-dependent stochastic Volterra integral equations." Electron. J. Probab. 26 1 - 29, 2021.


Received: 25 May 2020; Accepted: 21 December 2020; Published: 2021
First available in Project Euclid: 23 March 2021

arXiv: 1908.10786
Digital Object Identifier: 10.1214/20-EJP576

Primary: 28C20 , 45D05 , 45J05 , 60G17 , 60H20

Keywords: functional Itô calculus , functional Volterra integral equation , Hölder space , path-dependent Volterra process , support of a measure , vertical derivative


Vol.26 • 2021
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