Inequalities for the moments of stochastic integrals and stochastic Volterra equations driven a two-parameter Wiener process

N. A. Kolodii

Volgograd State University, Volgograd, Russia

Abstract: We prove existence and uniqueness theorems for a solution to a stochastic Volterra equation on the plane. The proofs employ an inequality for a stochastic integral with respect to a two-parameter Wiener process, where the integrand depends on the limits of integration.

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

UDC: 519.21

Received: 14.02.2008

 English version: Siberian Mathematical Journal, 2013, 54:5, 829–840

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