Geodesic
On a probability of simultaneously extremes of two Gaussian nonstationary processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 3, pp. 417-432

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This paper deals with the probability of simultaneous extremes of two Gaussian nonstationary processes $\mathbf{P}\bigl\{\max_{t\in[0,T]}X_1(t)>u,\ \max_{s\in[0,T]}X_2(s)>u\bigr\}$. The exact asymptotic representation for the probability is found as $u\to\infty$. The main tool for finding the asymptotics is a development of the double sum method.
Keywords: Gaussian nonstationary processes, extremum, double sum method. 
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     author = {A. Anshin},
     title = {On a probability of simultaneously extremes of two {Gaussian} nonstationary processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {417--432},
     publisher = {mathdoc},
     volume = {50},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2005_50_3_a0/}
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A. Anshin. On a probability of simultaneously extremes of two Gaussian nonstationary processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 3, pp. 417-432. http://geodesic.mathdoc.fr/item/TVP_2005_50_3_a0/