Open Access
July 2003 Integrated Brownian motions and exact $L_2$-small balls
F. Gao, J. Hannig, F. Torcaso
Ann. Probab. 31(3): 1320-1337 (July 2003). DOI: 10.1214/aop/1055425782


We will introduce a class of m-times integrated Brownian motions. The exact asymptotic expansions for the $L_2$-small ball probabilities will be discussed for members of this class, of which the usual m-times integrated Brownian motion is an example. Another example will be what we call an Euler-integrated Brownian motion. We will also find very sharp estimates for the asymptotics of the eigenvalues of the covariance operator of integrated Brownian motions and will, therefore, obtain exact, not just logarithmic, asymptotics.


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F. Gao. J. Hannig. F. Torcaso. "Integrated Brownian motions and exact $L_2$-small balls." Ann. Probab. 31 (3) 1320 - 1337, July 2003.


Published: July 2003
First available in Project Euclid: 12 June 2003

zbMATH: 1047.60030
MathSciNet: MR1989435
Digital Object Identifier: 10.1214/aop/1055425782

Primary: 60G15

Keywords: general integrated Brownian motion. , Small ball probability

Rights: Copyright © 2003 Institute of Mathematical Statistics

Vol.31 • No. 3 • July 2003
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