Density Bounds for Solutions to Differential Equations Driven by Gaussian Rough Paths
Density Bounds for Solutions to Differential Equations Driven by Gaussian Rough Paths
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DOI：
10.1007/s10959-019-00967-0
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发表时间：
2017-12
影响因子：
0.8
通讯作者：
B. Gess;Ouyang Cheng;S. Tindel
中科院分区：
文献类型：
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作者：
B. Gess;Ouyang Cheng;S. Tindel
我们考虑由中心高斯过程驱动的有限维粗糙微分方程。结合Malliavin微积分、粗糙路径技术和插值不等式，建立了任意固定时间下对应解的密度上界。此外，我们还提供了小噪声下密度渐近行为的Varadhan估计。重点是处理协方差函数满足适当抽象、可检出条件的一般高斯过程。
We consider finite-dimensional rough differential equations driven by centered Gaussian processes. Combining Malliavin calculus, rough paths techniques and interpolation inequalities, we establish upper bounds on the density of the corresponding solution for any fixed time. In addition, we provide Varadhan estimates for the asymptotic behavior of the density for small noise. The emphasis is on working with general Gaussian processes with covariance function satisfying suitable abstract, checkable conditions.