Integrated Brownian motions and exact L2-small balls
成果类型：
Article
署名作者：
Gao, F; Hannig, J; Torcaso, F
署名单位：
University of Idaho; Colorado State University System; Colorado State University Fort Collins; Johns Hopkins University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2003
页码：
1320-1337
关键词：
摘要：
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.