Application of the theory of square-Gaussian processes to simulation of stochastic processes

Abstract

In the paper the simulation of stochastic processes is considered. For this purpose the estimation for distribution of supremum of square-Gaussian processes is found. The theorems are proved that give the conditions under which the constructed model approximates stochastic process in Banach space with given accuracy and reliability. The obtained results can be widely used in actuarial science and financial mathematics.