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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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.

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

First available in Project Euclid: 10 May 2007

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

Anticipating stochastic calculus rough paths


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.

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