Maxima of Asymptotically Gaussian Random Fields and Moderate Deviation Approximations to Boundary-crossing Probabilities of Sums of Random Variables with Multidimensional Indices by Hock Peng Chan and Tze
نویسنده
چکیده
Several classical results on boundary-crossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices, multivariate empirical processes, and scan statistics in change-point and signal detection as special cases. Some key ingredients in these extensions are moderate deviation approximations to marginal tail probabilities and weak convergence of the conditional distributions of certain “clumps” around high-level crossings. We also discuss how these results are related to the Poisson clumping heuristic and tube formulas of Gaussian random fields, and describe their applications to laws of the iterated logarithm in the form of the Kolmogorov– Erdős–Feller integral tests. Short Title. MAXIMA OF RANDOM FIELDS Research supported by the National University of Singapore. Research supported by the National Science Foundation and the Institute of Mathematical Research at The University of Hong Kong. AMS 2000 subject classifications. Primary 60F10, 60G60; Secondary 60F20, 60G15.
منابع مشابه
Maxima of Asymptotically Gaussian Random Fields and Moderate Deviation Approximations to Boundary Crossing Probabilities of Sums of Random Variables with Multidimensional Indices
Several classical results on boundary crossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices, multivariate empirical processes, and scan statistics in change-point and signal detection as special cases. Some key ingredients in these extensions are moderate devia...
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