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

A. I. Nazarov   ; Ya. Yu. Nikitin

Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 695-711

Résumé

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.

Détail

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

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