Good Rough Path Sequences and Applications to Anticipating & Fractional Stochastic Calculus

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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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Probability, 60H99

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http://salesiana.dossiersoluciones.com/handle/123456789/73840

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0501197
 http://arxiv.org/abs/math/0501197

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arXiv