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arXiv · 0707.4546

Good rough path sequences and applications to anticipating stochastic calculus

Laure Coutin·Peter Friz·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.

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Laure Coutin, Peter Friz, Nicolas Victoir. 2007-07-31. Good rough path sequences and applications to anticipating stochastic calculus. https://doi.org/10.1214/009117906000000827

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