Construction of Approximate Formulas for Functionals of the Wiener and Some Other Processes and Also Numerical Examples

Abstract

In this paper for real Gaussian stochastic processes including Brownian bridge the approximate formulas for calculating its expectation values and dispersions are obtained. Numerical examples of calculation of the expectation values for the specific functions of stochastic Ornstein-Uhlenbeck process are constructed. A class of stochastic processes, the mathematical expectation of which is defined by Bernstein polynomials is considered. E. V. Voronovskaya’s formula concerning the asymptotic specification of function approximations by Bernstein polynomials has been applied for this case.