Good rough path sequences and applications to anticipating stochastic calculus

• 成果类型: Article
• 署名作者: Coutin, Laure; Friz, Peter; Victoir, Nicolas
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Cambridge; University of Oxford
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000827
• 发表日期: 2007
• 页码: 1172-1193
• 关键词: differential-equations; large deviations

摘要

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.