Nonlinear Phenomena in Complex Systems, 2017, Vol.20, No.3, pp. 258

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2017, Vol.20, No.3, pp. 258 - 266

Construction of Approximate Formulas for Functionals of the Wiener and Some Other Processes and also Numerical Examples
Leonid Yanovich and Andrei Khudyakov

WIn 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.

Key words: stochastic process, standard Wiener process, Brownian bridge, average, variance, approximation

Full text: Acrobat PDF (408 KB)