Non-degeneracy of Wiener functionals arising from rough differential equations
Non-degeneracy of Wiener functionals arising from rough differential equations
复制标题
由粗微分方程引起的维纳泛函的非简并性
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
Nicolas Victoir
中科院分区：
文献类型：
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作者：
T. Cass;P. Friz;Nicolas Victoir
Malliavin演算是关于Wiener空间上泛函的Sobolev型正则性的，主要的例子是通过求解随机微分方程得到的Ito映射。粗糙路径分析是关于（可能是随机的）微分方程解的强正则性。我们结合联合收割机的论点，这两个理论和讨论的存在性密度的随机微分方程的解驱动的一般类的非退化高斯过程，包括过程的样本路径正则性比布朗运动。
Malliavin Calculus is about Sobolev-type regularity of functionals on Wiener space, the main example being the Ito map obtained by solving stochastic differential equations. Rough path analysis is about strong regularity of the solution to (possibly stochastic) differential equations. We combine arguments of both theories and discuss the existence of a density for solutions to stochastic differential equations driven by a general class of non-degenerate Gaussian processes, including processes with sample path regularity worse than Brownian motion.