Anticipating stochastic Volterra equations

Elisa Alòs and David Nualart

Stochastic Processes and their Applications, 1997, vol. 72, issue 1, 73-95

Abstract: In this paper we establish the existence and uniqueness of a solution for stochastic Volterra equations assuming that the coefficients F(t,s,x) and Gi(t,s,x) are Ft-measurable, for s[less-than-or-equals, slant]t, where {Ft} denotes the filtration generated by the driving Brownian motion. We impose some differentiability assumptions on the coefficients, in the sense of the Malliavin calculus, in the time interval [s,t]. Some properties of the solution are discussed.

Date: 1997
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