Extremes of conditionally Gaussian processes

For a random element (X, Y) the component Y is called a random environment, and X is called a random element in the random environment if the properties of X are subject of primary interest, whereas the properties of Y can influence X.
Gaussian processes in a random environment, that is, Gaussian processes with random parameters (mean/trend, covariance), are called conditionally Gaussian processes, and they significantly extend the class of processes whose extremes can be studied with the techniques applied to Gaussian processes. For calculating the exact asymptotic behavior of the probability of large extremes of a conditionally Gaussian process, it is necessary to calculate this probability using fixed, non-random parameters, and then average the behavior over all the states of the parameter.
This talk gives a summary of our findings in this field.
Joint work with Sinisa Stamatovic.