Asymptotics of supremum distribution of [alpha](t)-locally stationary Gaussian processes

Krzysztof De[combining cedilla]bicki, and Pawel Kisowski

Stochastic Processes and their Applications, 2008, vol. 118, issue 11, 2022-2037

Abstract: We study the exact asymptotics of , as u-->[infinity], for centered Gaussian processes with the covariance function satisfying as h-->0. The obtained results complement those already considered in the literature for the case of locally stationary Gaussian processes in the sense of Berman, where [alpha](t)[reverse not equivalent][alpha]. It appears that the behavior of [alpha](t) in the neighborhood of its global minimum on [0,S] significantly influences the asymptotics. As an illustration we work out the case of X(t) being a standardized multifractional Brownian motion.

Keywords: Exact; asymptotics; Gaussian; process; Local; stationarity; Multifractional; Brownian; motion (search for similar items in EconPapers)
Date: 2008
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