Estimating the probability of large surges in a randomly perturbed second-order dynamic system (Q1921500)

Problems of estimating the probability of large ``extremal'' deviations of a dynamic system excited by white noise can be partitioned into two types. The first include those cases in which the value of the coordinate of interest is determined at a single point; the second includes cases in which one monitors the value of a coordinate during a definite time interval. For the second type problem simple analytical formulas are given for a certain class of second order dynamic systems. Moreover, the results from a series of numerical experiments are reported.