LetX= (X(t))(t >= 0)(X(0) = 0) be a continuous centered Gaussian process on a probability space (omega,F,P), and let (Y-t)(t is an element of)[0,1] (Y-0= 0) be a continuous process (on the same probability space) with nondecreasing paths, independent ofX. Define the time-changed Gaussian processZ(t)=X(Y-t),t is an element of [0,1]. In this paper, we investigate a problem of finite-dimensional large deviations and a problem of pathwise large deviations for time-changed continuous Gaussian processes. As applications, we considered subordinated Gaussian processes.

中文翻译：

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时变高斯过程的一些大偏差原理

令X= (X(t))(t >= 0)(X(0) = 0) 是概率空间 (omega,F,P) 上的连续中心高斯过程，且令 (Yt)(t 是一个元素of)[0,1] (Y-0= 0) 是一个连续的过程（在相同的概率空间上），具有非递减路径，与 X 无关。定义时变高斯过程Z(t)=X(Yt)，t是[0,1]的元素。在本文中，我们研究了时变连续高斯过程的有限维大偏差问题和路径大偏差问题。作为应用，我们考虑了从属高斯过程。