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作者：Taylor, Jonathan E.; Vadlamani, Sreekar
作者单位：Stanford University; Tata Institute of Fundamental Research (TIFR); TIFR Centre for Applicable Mathematics (CAM), Bengaluru
摘要：In this work we consider infinite dimensional extensions of some finite dimensional Gaussian geometric functionals called the Gaussian Minkowsld functionals. These functionals appear as coefficients in the probability content of a tube around a convex set D subset of R-k under the standard Gaussian law N(0, I-kxk). Using these infinite dimensional extensions, we consider geometric properties of some smooth random fields in the spirit of [Random Fields and Geometry (2007) Springer] that can be ...
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作者：Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Goetze, Friedrich
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Bielefeld
摘要：An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.
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作者：Adler, Mark; Ferrari, Patrik L.; van Moerbeke, Pierre
作者单位：Brandeis University; University of Bonn
摘要：Consider a continuous time random walk in Z with independent and exponentially distributed jumps +/- 1. The model in this paper consists in an infinite number of such random walks starting from the complement of {-m, -m + 1, ... , m - 1, m} at time -t, returning to the same starting positions at time t, and conditioned not to intersect. This yields a determinantal process, whose gap probabilities are given by the Fredholm determinant of a kernel. Thus this model consists of two groups of rando...
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作者：Lytvynov, Eugene
作者单位：Swansea University
摘要：Let X be a locally compact Polish space and let in be a reference Radon measure on X. Let Gamma(X) denote the configuration space over X, that is, the space of all locally finite subsets of X. A point process on X is a probability measure on Gamma(X). A point process mu is called determinantal if its correlation functions have the form k((n)) (x(1), ... , x(n)) = det[K (x(i), x(j))](i, j=1, ... ,n). The function K(x, y) is called the correlation kernel of the determinantal point process mu. As...
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作者：Buraczewski, D.; Damek, E.; Mikosch, T.; Zienkiewicz, J.
作者单位：University of Wroclaw; University of Copenhagen
摘要：In this paper we prove large deviations results for partial sums constructed from the solution to a stochastic recurrence equation. We assume Kesten's condition [Acta Math. 131 (1973) 207-248] under which the solution of the stochastic recurrence equation has a marginal distribution with power law tails, while the noise sequence of the equations can have light tails. The results of the paper are analogs to those obtained by A. V. Nagaev [Theory Probab. Appl. 14 (1969) 51-64; 193-208] and S. V....
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作者：Huesmann, Martin; Sturm, Karl-Theodor
作者单位：University of Bonn
摘要：This paper is devoted to the study of couplings of the Lebesgue measure and the Poisson point process. We prove existence and uniqueness of an optimal coupling whenever the asymptotic mean transportation cost is finite. Moreover, we give precise conditions for the latter which demonstrate a sharp threshold at d = 2. The cost will be defined in terms of an arbitrary increasing function of the distance. The coupling will be realized by means of a transport map (allocation map) which assigns to e...
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作者：Harnett, Daniel; Nualart, David
作者单位：University of Kansas
摘要：The purpose of this paper is to establish the convergence in law of the sequence of midpoint Riemann sums for a stochastic process of the form f'(W), where W is a Gaussian process whose covariance function satisfies some technical conditions. As a consequence we derive a change-of-variable formula in law with a second order correction term which is an Ito integral of f ''(W) with respect to a Gaussian martingale independent of W. The proof of the convergence in law is based on the techniques o...
