Convergence rate estimates of distributions of extrema of compound cox processes with nonzero means to locationmixtures of normal laws

Mathematical models of catastrophically accumulating effects related to nonhomogeneous chaotic flows of extremal events are considered, namely, extrema of compound doubly stochastic Poisson processes (compound Cox processes) with nonzero expectation. Convergence rate estimates are obtained in limit theorems for extrema of compound Cox processes. An example is given of existence of nontrivial limit of one-dimensional distributions of extrema of such processes with infinite variance under normalization which is traditional for sums with finite variance.