On the distribution of the last exit time over a slowly growing linear boundary for a Gaussian process

Nikita Karagodin; Mikhail Lifshits

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arXiv · 2012.03222

On the distribution of the last exit time over a slowly growing linear boundary for a Gaussian process

Nikita Karagodin·Mikhail Lifshits

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Abstract

For a class of Gaussian stationary processes, we prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly growing linear boundary. The limit is a double exponential (Gumbel) distribution.

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Nikita Karagodin, Mikhail Lifshits. 2020-12-06. On the distribution of the last exit time over a slowly growing linear boundary for a Gaussian process. https://arxiv.org/abs/2012.03222

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