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Good Rough Path Sequences and Applications to Anticipating & Fractional 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 (not necessarily a semi-martingale). No adaptedness of initial point or vector fields 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. This condition is satisfied by the Brownian motion and the fractional Brownian motion with Hurst parameter greater than 1/4. As application, we obtain rather flexible results such as support theorems, large deviation principles and Wong-Zakai approximations for SDEs driven by fractional Brownian Motion along anticipating vectorfields. In particular, this unifies many results on anticipative SDEs.

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Laure Coutin, Peter Friz, Nicolas Victoir. 2005-01-13. Good Rough Path Sequences and Applications to Anticipating & Fractional Stochastic Calculus. https://arxiv.org/abs/math/0501197

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