Extremes of Gaussian chaos processes with trend

Let X(t) (X-1 (t), ..., X-d(t)), t is an element of [0, S] be a Gaussian vector process and let g(x), x is an element of R-d be a continuous homogeneous function. We are concerned with the exact tail asymptotic of the chaos process g(X(t)), t is an element of [0, S] with a trend function h(t). Both scenarios X(t) is locally-stationary and X(t) is non-stationary are considered. Important examples include the product of Gaussian processes and chi-processes. (C) 2019 Elsevier Inc. All rights reserved.