Good rough path sequences and applications to anticipating stochastic calculus
Good rough path sequences and applications to anticipating stochastic calculus
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良好的粗略路径序列及其在预测随机微积分中的应用
DOI：
10.1214/009117906000000827
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发表时间：
2007
影响因子：
2.3
通讯作者：
Nicolas Victoir
中科院分区：
文献类型：
--
作者：
L. Coutin;P. Friz;Nicolas Victoir
考虑一类随机过程驱动的Stratonovich随机微分方程提升到粗糙路径上，不需要初始点和向量场的自适应性，也不需要向量场之间的交换条件.在随机过程的一个简单条件下，我们证明了在粗糙路径意义下的上述解的唯一解实际上是Stratonovich解。然后，我们证明了布朗运动满足这个条件。作为应用，我们得到了布朗运动沿着期望向量场驱动的偏微分方程的支撑定理、大偏差原理和Wong-Zakai逼近等相当灵活的结果.特别是，这统一了许多预期的SDES的结果。
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.