Accuracy and reliability of models of stochastic processes of the space \(\text{Sub}_{\varphi}(\Omega)\). (Ukrainian, English) Zbl 1100.60016

Kozachenko, Yu. V.; Rozora, I. V.

Teor. Jmovirn. Mat. Stat. 71, 93-104 (2004); translation in Theory Probab. Math. Stat. 71, 105-117 (2005).

The authors deal with stationary stochastic processes from the space \(\text{Sub}_{\varphi}(\Omega)\). For such processes inequalities for the large deviation probabilities are obtained. Models which approximate a process from \(\text{Sub}_{\varphi}(\Omega)\) with a given accuracy and reliability in the Banach space \(C[0,1]\) are constructed. Sufficient conditions are obtained under which a model approximates a sub-Gaussian process with a given accuracy and reliability in the Banach space \(C[0,1]\).

Reviewer: A. D. Borisenko (Kyïv)

MSC:

60G10	Stationary stochastic processes
68U20	Simulation (MSC2010)

Keywords:

modelling of stochastic process