Optimal Prediction of Level Crossings in Gaussian Processes and Sequences
نویسندگان
چکیده
منابع مشابه
Level crossings and other level functionals of stationary Gaussian processes
Abstract: This paper presents a synthesis on the mathematical work done on level crossings of stationary Gaussian processes, with some extensions. The main results [(factorial) moments, representation into the Wiener Chaos, asymptotic results, rate of convergence, local time and number of crossings] are described, as well as the different approaches [normal comparison method, Rice method, Stein...
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Let (X,, t~ [0, 11) be a oentred stationary Gaussian process defined on (D, A, P) with covariance function satisfying Define the regularized process X' = cp, * X and YE = Xc/oe, where CT~ = var Xf , cp8 is a kernel which approaches the Dirac delta function as c -+ 0 and * denotes the convolution. We study the convergence of where NV(x) and L,(x) denote, respectively, the number of crossings and...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1985
ISSN: 0091-1798
DOI: 10.1214/aop/1176992909