A limit theorem for the last exit time over a moving nonlinear boundary for a Gaussian process
Abstract
We prove a limit theorem on the convergence of the distributions 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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2021
- DOI:
- 10.48550/arXiv.2110.01046
- arXiv:
- arXiv:2110.01046
- Bibcode:
- 2021arXiv211001046K
- Keywords:
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- Mathematics - Probability
- E-Print:
- 20 pages. Revised structure and fixed typos, results unchanged. arXiv admin note: substantial text overlap with arXiv:2012.03222