The Annals of Probability

Good rough path sequences and applications to anticipating stochastic calculus

Laure Coutin, Peter Friz, and Nicolas Victoir

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Abstract

We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process lifted to a rough path. Neither adaptedness of initial point and vector fields nor commuting conditions between vector field is assumed. Under a simple condition on the stochastic process, we show that the unique solution of the above SDE understood in the rough path sense is actually a Stratonovich solution. We then show that this condition is satisfied by the Brownian motion. As application, we obtain rather flexible results such as support theorems, large deviation principles and Wong–Zakai approximations for SDEs driven by Brownian motion along anticipating vectorfields. In particular, this unifies many results on anticipative SDEs.

Article information

Source
Ann. Probab., Volume 35, Number 3 (2007), 1172-1193.

Dates
First available in Project Euclid: 10 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1178804326

Digital Object Identifier
doi:10.1214/009117906000000827

Mathematical Reviews number (MathSciNet)
MR2319719

Zentralblatt MATH identifier
1132.60053

Subjects
Primary: 60H99: None of the above, but in this section

Keywords
Anticipating stochastic calculus rough paths

Citation

Coutin, Laure; Friz, Peter; Victoir, Nicolas. Good rough path sequences and applications to anticipating stochastic calculus. Ann. Probab. 35 (2007), no. 3, 1172--1193. doi:10.1214/009117906000000827. https://projecteuclid.org/euclid.aop/1178804326


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