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作者：Fan, Zhou; Johnstone, Iain M.
作者单位：Yale University; Stanford University
摘要：We study the sample covariance matrix for real-valued data with general population covariance, as well as MANOVA-type covariance estimators in variance components models under null hypotheses of global sphericity. In the limit as matrix dimensions increase proportionally, the asymptotic spectra of such estimators may have multiple disjoint intervals of support, possibly intersecting the negative half line. We show that the distribution of the extremal eigenvalue at each regular edge of the sup...
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作者：Chen, Yu-Ting
作者单位：University of Victoria
摘要：We study some SDEs derived from the q -> 1 limit of a 2D surface growth model called the q-Whittaker process. The fluctuations are proven to exhibit Gaussian characteristics that come down from infinity: After rescaling and re-centering, convergences to the time-inverted stationary additive stochastic heat equation (SHE) hold. The point of view in this paper is a novel probabilistic representation of the SDEs by independent sums. By this connection, the normal and Poisson approximations, both ...
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作者：Ernst, Philip A.; Peskir, Goran
作者单位：Rice University; University of Manchester
摘要：Consider the motion of a Brownian particle in two or more dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservable time, one of the coordinate processes gets a (known) nonzero drift permanently. Given that the position of the Brownian particle is being observed in real time, the problem is to detect the time at which a coordinate process gets the drift as accurately as possible. We solve this problem in the most uncert...
