Maxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices

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

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...

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...

Large-deviation Probabilities for Maxima of Sums of Independent Random Variables with Negative Mean and Subexponential Distribution∗

Abstract. We consider the sums Sn = ξ1 + · · · + ξn of independent identically distributed random variables with negative mean value. In the case of subexponential distribution of the summands, the asymptotic behavior is found for the probability of the event that the maximum of sums max(S1, . . . , Sn) exceeds high level x. The asymptotics obtained describe this tail probability uniformly with...

Expected Number of Local Maxima of Some Gaussian Random Polnomials

Maxima of sums and random sums for negatively associated random variables with heavy tails

This paper obtains some asymptotics for the tail probabilities of the maximum of sums and random sums of negatively associated (NA) random variables with heavy tails, showing that the NA dependence structure does not affect the asymptotic behavior of these tail probabilities. r 2004 Elsevier B.V. All rights reserved.