Background. Random process theory is being used more and more in various fields of science due to the high computing power of modern computers. However, it's often important to know how much we can rely on the models we use. Methods. This paper examines the modelling of the fractional Brownian motion with given accuracy and reliability. The modelling is based on Dzhaparidze and van Zanten series representation of the fractional Brownian motion. We consider the fractional Brownian motion as an input process to a time-invariant linear system with a real-valued square-integrable impulse response function, which is defined on the finite domain. Results. We prove the theorem that gives the conditions, specifically the value of the upper limit of the summing in the model, under which the obtained model approximates fractional Brownian motion with given accuracy and reliability taking into account the response of the system. Conclusions. For the proof, we use the properties of square-Gaussian stochastic processes.

Iryna Rozora

Simulation of the fractional Brownian process with given accuracy and reliability

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