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 $$t>0$$ t > 0 . 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.

中文翻译：

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由高斯粗糙路径驱动的微分方程解的密度界

我们考虑由中心高斯过程驱动的有限维粗微分方程。结合 Malliavin 演算、粗糙路径技术和插值不等式，我们建立了任何固定时间 $$t>0$$t>0 对应解的密度的上限。此外，我们提供了对小噪声密度渐近行为的 Varadhan 估计。重点是处理具有满足合适抽象、可检查条件的协方差函数的一般高斯过程。