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May 2007 Good rough path sequences and applications to anticipating stochastic calculus
Laure Coutin, Peter Friz, Nicolas Victoir
Ann. Probab. 35(3): 1172-1193 (May 2007). DOI: 10.1214/009117906000000827

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.

Citation

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Laure Coutin. Peter Friz. Nicolas Victoir. "Good rough path sequences and applications to anticipating stochastic calculus." Ann. Probab. 35 (3) 1172 - 1193, May 2007. https://doi.org/10.1214/009117906000000827

Information

Published: May 2007
First available in Project Euclid: 10 May 2007

zbMATH: 1132.60053
MathSciNet: MR2319719
Digital Object Identifier: 10.1214/009117906000000827

Subjects:
Primary: 60H99

Keywords: anticipating stochastic calculus , Rough paths

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 3 • May 2007
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