Good rough path sequences and applications to anticipating stochastic calculus

Details Good rough path sequences and applications to anticipating stochastic calculus Good rough path sequences and applications to anticipating stochastic calculus

2007-07-31

arxiv.org/abs/0707.4546v1

Annals of Probability 2007, Vol. 35, No. 3, 1172-1193

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000827 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000827

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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