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作者：Feldheim, Ohad Noy; Gurel-Gurevich, Ori; Li, Jiange
作者单位：Hebrew University of Jerusalem; Harbin Institute of Technology
摘要：In the two-thinning balls-and-bins model, an overseer is provided with uniform random allocation of m balls into n bins in an on-line fashion. The overseer may reject the allocation of each ball, in which case it is placed into a new bin, drawn independently, uniformly at random. The purpose of the overseer is to reduce the maximum load, that is, the difference between the maximum number of balls in a single bin and the average number of balls among all bins. We provide tight estimates for thr...
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作者：Goldenshluger, Alexander; Jacobovic, Royi
作者单位：University of Haifa
摘要：Suppose that particles are randomly distributed in R-d, and they are subject to identical stochastic motion independently of each other. The Smoluchowski process describes fluctuations of the number of particles in an observation region over time. This paper studies properties of the Smoluchowski processes and considers related statistical problems. In the first part of the paper we revisit probabilistic properties of the Smoluchowski process in a unified and principled way: explicit formulas ...
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作者：Appuhamillage, Thilanka; Bokil, Vrushali; Thomann, Enrique; Waymire, Edward; Wood, Brian
作者单位：HSBC Holdings; Oregon State University; Oregon State University
摘要：The failure of a symmetry argument for the Laplace transform of a mul-tivariate density given inAnn. Appld. Probab.21(1) (2011), 183-214 wasneglected in preparation of the first errata (Ann. Appld. Probab.21(5) (2011),2050-2051). The formula for the Laplace transform is corrected in this errata
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作者：Hocquet, Antoine; Neamtu, Alexandra
作者单位：Technical University of Berlin; University of Konstanz
摘要：We investigate the abstract Cauchy problem for a quasilinear parabolic equation in a Banach space of the form dut - Lt(ut)ut dt = Nt(ut)dt + F(ut) d X t , where X is a gamma-H & ouml;lder rough path for gamma E ( 1 / 3 , 1/2). We explore the mild formulation that combines functional analysis techniques and controlled rough paths theory which entail the local well-posedness of such equations. We apply our results to the stochastic Landau-Lifshitz-Gilbert and Shigesada-Kawasaki-Teramoto equation.
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作者：Costantini, Cristina; Kurtz, Thomas G.
作者单位：G d'Annunzio University of Chieti-Pescara; G d'Annunzio University of Chieti-Pescara; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
摘要：Bass and Pardoux ( Probab. Theory Related Fields (1987) 76 557-572) deduce from the Krein-Rutman theorem a reverse ergodic theorem for a sub- probability transition function, which turns out to be a key tool in proving uniqueness of reflecting Brownian motion in cones in Kwon and Williams ( Trans. Amer. Math. Soc (1991) 32 739-780) and Taylor and Williams ( Probab. Theory Related Fields (1993) 96 283-317). By a different approach, we are able to prove an analogous reverse ergodic theorem for a...
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作者：Benth, Fred espen; Schroers, Dennis; Veraart, Almut e. d.
作者单位：University of Oslo; Imperial College London
摘要：This article establishes an asymptotic theory for volatility estimation in an infinite -dimensional setting. We consider mild solutions of semilinear stochastic partial differential equations and derive a stable central limit theorem for the semigroup-adjusted realised covariation (SARCV), which is a consistent estimator of the integrated volatility and a generalisation of the realised quadratic covariation to Hilbert spaces. Moreover, we introduce semigroup-adjusted multipower variations (SAM...
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作者：Dello Schiavo, Lorenzo; Portinale, Lorenzo; Sau, Federico
作者单位：Institute of Science & Technology - Austria; University of Bonn; University of Catania
摘要：We consider the open symmetric exclusion (SEP) and inclusion (SIP) processes on a bounded Lipschitz domain Omega, with both fast and slow boundary. For the random walks on Omega dual to SEP/SIP we establish: a functional-CLT-type convergence to the Brownian motion on Omega with either Neumann (slow boundary), Dirichlet (fast boundary), or Robin (at criticality) boundary conditions; the discrete-to-continuum convergence of the corresponding harmonic profiles. As a consequence, we rigorously der...
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作者：Peca-Medlin, John
作者单位：University of Arizona
摘要：Gaussian elimination with partial pivoting (GEPP) is a widely usedmethod to solve dense linear systems. Each GEPP step uses a row transposi-tion pivot movement if needed to ensure the leading pivot entry is maximalin magnitude for the leading column of the remaining untriangularized sub-system. We will use theoretical and numerical approaches to study how oftenthis pivot movement is needed. We provide full distributional descriptions forthe number of pivot movements needed using GEPP using par...
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作者：Wang, Zhichao; Zhu, Yizhe
作者单位：University of California System; University of California San Diego; University of California System; University of California Irvine
摘要：In this paper, we investigate a two -layer fully connected neural network of the form f (X) = 1/root d(1) a(T )sigma (W X ), where X is an element of (d0xn) is a deterministic data matrix, W is an element of R-d1xd0 and a is an element of R-d1 are random Gaussian weights, and sigma is a nonlinear activation function. We study the limiting spectral distributions of two empirical kernel matrices associated with f (X): the empirical conjugate kernel (CK) and neural tangent kernel (NTK), beyond th...
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作者：Birkner, Matthias; Dahmer, Iulia; Diehl, Christina S.; Kersting, Goetz
作者单位：Johannes Gutenberg University of Mainz; Goethe University Frankfurt
摘要：We consider Beta(2 - alpha, alpha)-coalescents with parameter range 1 < alpha < 2 starting from n leaves. The length l(r)((n)) of order r in the n-Beta(2 - alpha, alpha)-coalescent tree is defined as the sum of the lengths of all branches that carry a subtree with r leaves. We show that for any s is an element of N the vector of suitably centered and rescaled lengths of orders 1 <= r <= s converges in distribution to a multivariate stable distribution as the number of leaves tends to infinity.
