The Annals of Probability

Stochastic Volterra Equations with Anticipating Coefficients

Etienne Pardoux and Philip Protter

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Abstract

Stochastic Volterra equations are studied where the coefficients $F(t, s, x)$ are random and adapted to $\mathscr{F}_{s\vee t}$ rather than the customary $\mathscr{F}_{s\wedge t}$. Such a hypothesis, which is natural in several applications, leads to stochastic integrals with anticipating integrands. We interpret these as Skorohod integrals, which generalize Ito's integrals to the case where the integrand anticipates the future of the Wiener integrator. We shall nevertheless construct an adapted solution, which is even a semimartingale if the coefficients are smooth enough.

Article information

Source
Ann. Probab., Volume 18, Number 4 (1990), 1635-1655.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990638

Digital Object Identifier
doi:10.1214/aop/1176990638

Mathematical Reviews number (MathSciNet)
MR1071815

Zentralblatt MATH identifier
0717.60073

JSTOR
links.jstor.org

Subjects
Primary: 60H20: Stochastic integral equations
Secondary: 60H05: Stochastic integrals

Keywords
Stochastic Volterra equations anticipating stochastic calculus Skorohod integral

Citation

Pardoux, Etienne; Protter, Philip. Stochastic Volterra Equations with Anticipating Coefficients. Ann. Probab. 18 (1990), no. 4, 1635--1655. doi:10.1214/aop/1176990638. https://projecteuclid.org/euclid.aop/1176990638


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