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Small ball probabilities for Gaussian processes with stationary increments under Hölder norms |
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| Authors: | J Kuelbs W V Li Qi-man Shao |
| Institution: | (1) Department of Mathematics, University of Wisconsin-Madison, 53706 Madison, Wisconsin;(2) Department of Mathematical Sciences, University of Delaware, 19716 Newark, Delaware;(3) Department of Mathematics, National University of Singapore, 0511, Singapore |
| Abstract: | Small ball probabilities are estimated for Gaussian processes with stationary increments when the small balls are given by various Hölder norms. As an application we establish results related to Chung's functional law of the iterated logarithm for fractional Brownian motion under Hölder norms. In particular, we identify the points approached slowest in the functional law of the iterated logarithm.Supported in part by NSF Grant DMS-9024961. |
| Keywords: | Gaussian processes small ball probabilities the law of the iterated logarithm |
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