Densities for rough differential equations under Hormander's condition
成果类型：
Article
署名作者：
Cass, Thomas; Friz, Peter
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
发表日期：
2010
页码：
2115-2141
关键词：
摘要：
We consider stochastic differential equations dY = V (Y) dX driven by a multidimensional Gaussian process X in the rough path sense [ T. Lyons, Rev. Mat. Iberoamericana 14, (1998), 215-310]. Using Malliavin Calculus we show that Y-t admits a density for t is an element of (0, T] provided (i) the vector fields V = (V-1,...,V-d) satisfy Hormander's condition and (ii) the Gaussian driving signal X satisfies certain conditions. Examples of driving signals include fractional Brownian motion with Hurst parameter H > 1/4, the Brownian bridge returning to zero after time T and the Ornstein-Uhlenbeck process.