Geodesic
On the distribution of the last exit time over a~slowly growing linear boundary for a~Gaussian process
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 419-432

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: last exit time, Gaussian process, limit theorem, double exponential law. 
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     author = {N. A. Karagodin and M. A. Lifshits},
     title = {On the distribution of the last exit time over a~slowly growing linear boundary for {a~Gaussian} process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {419--432},
     publisher = {mathdoc},
     volume = {66},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a0/}
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N. A. Karagodin; M. A. Lifshits. On the distribution of the last exit time over a~slowly growing linear boundary for a~Gaussian process. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 419-432. http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a0/