, Volume 101, Issue 2, pp 173-192

Small values of Gaussian processes and functional laws of the iterated logarithm

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Summary

We estimate small ball probabilities for locally nondeterministic Gaussian processes with stationary increments, a class of processes that includes the fractional Brownian motions. These estimates are used to prove Chung type laws of the iterated logarithm.

Research supported by the United States Air Force office of Scientific Research, Contract No. 91-0030