The Distribution of the Largest Values in the Realization of Random Processes with Discrete Time

An expression is given for the distribution of the duration of intervals between peaks of a stationary normal-random process in terms of the limiting distribution of its absolute maximum for large intervals. A general expression is determined for the probability density of the largest values in realizations of random processes with discrete time (random sequences); an approximation of this expression, based on the properties of multiply connected Markov chains, is given. As an example the distribution of the largest values in realizations of a stationary Rayleigh sequence is calculated approximately.