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Extremes of $ \alpha(\boldsymbol{t})$-locally stationary Gaussian random fields


Authors: Enkelejd Hashorva and Lanpeng Ji
Journal: Trans. Amer. Math. Soc. 368 (2016), 1-26
MSC (2010): Primary 60G15; Secondary 60G70
DOI: https://doi.org/10.1090/tran/6769
Published electronically: September 10, 2015
MathSciNet review: 3413855
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Abstract: The main result of this contribution is the derivation of the exact asymptotic behavior of the supremum of a class of $ \alpha (\mathbf {t})$-locally stationary Gaussian random fields. We present two applications of our result: the first one deals with the extremes of aggregate multifractional Brownian motions, whereas the second one establishes the exact asymptotics of the supremum of the $ \chi $-process generated by multifractional Brownian motions.


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Additional Information

Enkelejd Hashorva
Affiliation: Department of Actuarial Science, University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland

Lanpeng Ji
Affiliation: Department of Actuarial Science, University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland

DOI: https://doi.org/10.1090/tran/6769
Keywords: $\alpha(\boldsymbol{t})$-locally stationary random fields, fractional Brownian motion, multifractional Brownian motion, $\chi$-processes, Gaussian random fields, metric entropy, weak convergence, Pickands constant
Received by editor(s): June 17, 2013
Published electronically: September 10, 2015
Article copyright: © Copyright 2015 American Mathematical Society