L. Beghin, Ya. Yu. Nikitin, E. Orsingher, “Exact small ball constants for some Gaussian processes under <nobr>$L^2$</nobr>-norm”, Zap. Nauchn. Sem. POMI, 2003, Volume 298,Pages <nobr>5

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Exact small ball constants for some Gaussian processes under $L^2$-norm

L. Beghin^a, Ya. Yu. Nikitin^b, E. Orsingher^a

^a Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma la Sapienza
^b St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: We find some logarithmic and exact small deviation asymptotics for the $L^2$-norm of certain Gaussian processes closely connected with the Wiener process. In particular the processes obtained by centering and integrating Brownian motion and Brownian bridge are examined.

UDC: 519.21

Received: 12.10.2003

Language: English