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Mat. Zametki, 2006 Volume 80, Issue 3, Pages 386–394 (Mi mzm2824)

Excursions of a Gaussian process with variable variance above a barrier increasing to infinity

S. G. Kobel'kov

M. V. Lomonosov Moscow State University

Abstract: For a family of real-valued Gaussian processes $\xi_u(t)$, $t\in[0,T]$, we obtain an exact asymptotics of the probability of crossing a level $u$ as $u\to\infty$ under certain conditions on the variance and correlation. This result is applied to the investigation of excursions of a stationary zero-mean process above a barrier increasing to infinity.

Keywords: Gaussian process, excursions of Gaussian processes, level-crossing probability, fractional Brownian motion, covariance function.

UDC: 519.218.7

Received: 14.01.2005

DOI: 10.4213/mzm2824


 English version:
Mathematical Notes, 2006, 80:3, 372–379

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