Simulations of standard Brownian motion

Anatolii Pashko 

Taras Shevchenko National University of Kyiv, Prospect Hlushkov, 4D, 03187 Kyiv, Ukraine

This paper investigates algorithms for simulation of the trajectories of a Brownian motion (Wiener process) with given accuracy and reliability. Spectral representation of Wiener process as random series examines as a model. Estimates of the accuracy and reliability investigated in various function spaces - spaces of measurable integrated functions, Orlicz spaces and spaces of continuous functions. Given the accuracy of the numbers and simulation algorithms error of Gaussian random variables in the model are used strictly sub-Gaussian random variables. Examples of simulation are represented below.