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International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 137271, 20 pages
http://dx.doi.org/10.1155/2012/137271
Research Article

Survival Exponents for Some Gaussian Processes

Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Profsoyuznaya 84/32, 117997 Moscow, Russia

Received 22 May 2012; Accepted 7 August 2012

Academic Editor: Yaozhong Hu

Copyright © 2012 G. Molchan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The problem is a power-law asymptotics of the probability that a self-similar process does not exceed a fixed level during long time. The exponent in such asymptotics is estimated for some Gaussian processes, including the fractional Brownian motion (FBM) in , and the integrated FBM in , .