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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 42, Fasc. 2,
pages 195 - 217
DOI: 10.37190/0208-4147.00043
Published online 14.10.2022
 

A limit theorem for the last exit time over a moving nonlinear boundary for a Gaussian process

N. Karagodin

Abstract: We prove the convergence of the distribution of the scaled last exit time over a slowly moving nonlinear boundary for a class of Gaussian stationary processes. The limit is a double exponential (Gumbel) distribution.

2010 AMS Mathematics Subject Classification: Primary 60G10; Secondary 60F05.

Keywords and phrases: last exit time, nonlinear boundary, Gaussian process, limit theorem, double exponential law.

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