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On small deviation probabilities for certain iterated random processes. (English. Russian original) Zbl 1297.93147

Vestn. St. Petersbg. Univ., Math. 46, No. 4, 180-186 (2013); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 2013, No. 3, 89-97 (2013).
Summary: The asymptotic behavior of small deviation probabilities for some iterated random processes is investigated. It is shown that, under certain conditions, iterated and noniterated processes have logarithmic asymptotics of the same character; otherwise, these asymptotics may differ substantially. Some iterated Gaussian processes are considered as an example.

MSC:

93E03 Stochastic systems in control theory (general)
60G15 Gaussian processes
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