Open Access
October, 1990 Stochastic Volterra Equations with Anticipating Coefficients
Etienne Pardoux, Philip Protter
Ann. Probab. 18(4): 1635-1655 (October, 1990). DOI: 10.1214/aop/1176990638


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.


Download Citation

Etienne Pardoux. Philip Protter. "Stochastic Volterra Equations with Anticipating Coefficients." Ann. Probab. 18 (4) 1635 - 1655, October, 1990.


Published: October, 1990
First available in Project Euclid: 19 April 2007

zbMATH: 0717.60073
MathSciNet: MR1071815
Digital Object Identifier: 10.1214/aop/1176990638

Primary: 60H20
Secondary: 60H05

Keywords: anticipating stochastic calculus , Skorohod integral , Stochastic Volterra equations

Rights: Copyright © 1990 Institute of Mathematical Statistics

Vol.18 • No. 4 • October, 1990
Back to Top