Abstract
Abstract We give definitions for random processes in random environment, in particular, Gaussian random processes in random environment, or, in other words, conditionally Gaussian processes. With some constrains on a random environment, we formulate the large deviation principle for Gaussian processes in the random environment. Further, we consider a class of Gaussian processes in random environment that allows exact calculations for probabilities of large extremes. This is a class of Gaussian stationary processes with smooth bounded random stationary variance. We show how the random environment affects on such probabilities.
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