Simulation of Pickands constants

Krzysztof Burnecki and Zbigniew Michna

No HSC/02/03, HSC Research Reports from Hugo Steinhaus Center, Wroclaw University of Science and Technology

Abstract: Pickands constants appear in the asymptotic formulas for extremes of Gaussian processes. The explicit formula of Pickands constants does not exist. Moreover, in the literature there is no numerical approximation. In this paper we compute numerically Pickands constants by the use of change of measure technique. To this end we apply two different algorithms to simulate fractional Brownian motion. Finally, we compare the approximations with a theoretical hypothesis and a recently obtained lower bound on the constants. The results justify the hypothesis.

Keywords: Pickands constant; fractional Brownian motion; change of measure; Cholesky factorization; fGp algorithm (search for similar items in EconPapers)
JEL-codes: C15 C63 (search for similar items in EconPapers)
Pages: 8 pages
Date: 2002
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Citations: View citations in EconPapers (2)

Published in Probability and Mathematical Statistics 22.1 (2002) 193-199.

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http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_02_03.pdf Final draft, 2002 (application/pdf)
http://www.math.uni.wroc.pl/~pms/files/22.1/Article/22.1.14.pdf Final printed version, 2002 (application/pdf)

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