论文标题
由单数协方差高斯流程驱动的粗糙路径和对称 - 斯特拉托维奇积分
Rough paths and symmetric-Stratonovich integrals driven by singular covariance gaussian processes
论文作者
论文摘要
我们研究了在正规化意义上的对称 - 斯特拉托尼维奇积分之间的随机版本的随机版本之间的关系。在Malliavin微积分的意义上，在轻度的规律性条件下，我们在随机粗糙路径和由一类高斯过程驱动的随机粗糙路径和对称性 - 斯特拉托维奇积分之间建立平等。作为一种副产品，我们表明，由大型高斯粗糙路径驱动的多维粗糙微分方程的解决方案实际上是Stratonovich随机微分方程的解决方案。我们获得了一阶Stratonovich方案的几乎确定的收敛速率，从Gubinelli意义上讲，对粗略的路径积分。如果集成媒体的Malliavin衍生物的时间增加足够规律，则速率基本上是较高的。该框架适用于大型高斯过程，其协方差函数的二阶导数是$ {\ Mathbb r}^2 $ +对角线上的Sigma-Finite非阳性度量。
We examine the relation between a stochastic version of the rough path integral with the symmetric-Stratonovich integral in the sense of regularization. Under mild regularity conditions in the sense of Malliavin calculus, we establish equality between stochastic rough path and symmetric-Stratonovich integrals driven by a class of Gaussian processes. As a by-product, we show that solutions of multi-dimensional rough differential equations driven by a large class of Gaussian rough paths they are actually solutions to Stratonovich stochastic differential equations. We obtain almost sure convergence rates of the first-order Stratonovich scheme to rough paths integrals in the sense of Gubinelli. In case the time-increment of the Malliavin derivative of the integrands is regular enough, the rates are essentially sharp. The framework applies to a large class of Gaussian processes whose the second-order derivative of the covariance function is a sigma-finite non-positive measure on ${\mathbb R}^2$ + off diagonal.
