I. A. Duchitskii, V. Yu. Korolev, I. A. Sokolov, “On the accuracy of some mathematical models of catastrophically accumulated effects in prediction of risks of extremal events”, Inform. Primen., 2012, Volume 6, Issue 4,Pages <nobr>9

On the accuracy of some mathematical models of catastrophically accumulated effects in prediction of risks of extremal events

I. A. Duchitskii^a, V. Yu. Korolev^ab, I. A. Sokolov^b

^a M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
^b Institute for Problems of Informatics of RAS

Abstract: Estimates are constructed for the accuracy of approximation of the distributions of extrema of special random sums by scale mixtures of half-normal laws. The possibility of the application of these results in prediction of risks of extremal events due to catastrophically accumulated effects is discussed.

Keywords: nonhomogeneous flows of events; doubly stochastic Poisson process; negative binomial distribution; gamma-distribution; convergence rate estimate.