Existence and continuity with respect to parameter of solutions to stochastic Volterra equations in a plane

N. A. Kolodii

Chair of Fundamental Information Science and Optimal Control, Volgograd State University, Volgograd, Russia

Abstract: In this paper we study stochastic Volterra equations in the plane. These equations contain integrals with respect to local bounded variation fields and square-integrable strong martingales. We prove the existence and uniqueness of solutions of such equations with local integrable (in some measure) trajectories, assuming that the coefficients of equations possess the Lipschitz property with respect to the functional argument. We prove that the solution of a stochastic Volterra integral equation in the plane is continuous with respect to the parameter.

Keywords: two-parameter martingale, stochastic Volterra equation, stopping line.

UDC: 519.21

Received: 02.11.2007

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:2, 16–27

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