A. I. Nazarov, Ya. Yu. Nikitin, “Logarithmic <nobr>$L_2$</nobr>-small ball asymptotics for some fractional Gaussian processes”, Teor. Veroyatnost. i Primenen., 2004, Volume 49, Issue 4,Pages <nobr>695

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Logarithmic $L_2$-small ball asymptotics for some fractional Gaussian processes

A. I. Nazarov, Ya. Yu. Nikitin

St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: We find the logarithmic $L_2$-small ball asymptotics of some Gaussian processes related to the fractional Brownian motion (fBm), fractional Ornstein–Uhlenbeck process (fOU), and their integrated analogues. We consider also the multiparameter generalizations.

Keywords: fractional Brownian motion, fractional Ornstein–Uhlenbeck process, Lévy's Brownian motion, small deviations, spectral asymptotics.

Received: 17.05.2004

DOI: 10.4213/tvp189