-
作者：Hsing, T; Wu, WB
作者单位：Texas A&M University System; Texas A&M University College Station; University of Chicago
摘要：A weighted U-statistic based on a random sample X-1,..., X-n has the form U-n = Sigma(1less than or equal toi, jless than or equal ton) w(i-j) K(X-i, X-j), where K is a fixed symmetric measurable function and the w(i) are symmetric weights. A large class of statistics can be expressed as weighted U-statistics or variations thereof. This paper establishes the asymptotic normality of U-n when the sample observations come from a nonlinear time series and linear processes.
-
作者：Attal, SP; Lindsay, JM
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Nottingham
摘要：Quantum stochastic calculus is extended in a new formulation in which its stochastic integrals achieve their natural and maximal domains. Operator adaptedness, conditional expectations and stochastic integrals are all defined simply in terms of the orthogonal projections of the time filtration of Fock space, together with sections of the adapted gradient operator. Free from exponential vector domains, our stochastic integrals may be satisfactorily composed yielding quantum Ito formulas for ope...
-
作者：Dalang, RC; Lévêque, O
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We study a class of linear hyperbolic stochastic partial differential equations in bounded domains, which includes the wave equation and the telegraph equation, driven by Gaussian noise that is white in time but not in space. We give necessary and sufficient conditions on the spatial correlation of the noise for the existence (and uniqueness) of square-integrable solutions. In the particular case where the domain is a ball and the noise is concentrated on a sphere, we characterize the isotropi...
-
作者：Mathieu, P; Remy, E
作者单位：Aix-Marseille Universite
摘要：We prove that the heat kernel on the infinite Bernoulli percolation cluster in Z(d) almost surely decays faster than t(-d/2). We also derive estimates on the mixing time for the random walk confined to a finite box. Our approach is based on local isoperimetric inequalities. Some of the results of this paper were previously announced in the note of Mathieu and Remy.
-
作者：Kösters, H
作者单位：University of Munster
摘要：Let X-1, X-2,... be a sequence of [0, 1]-valued i.i.d. random variables, let c greater than or equal to 0 be a sampling cost for each observation and let Y-i = X-i - ic, i = 1, 2,.... For n = 1, 2,..., let M(Y-1,..., Y-n) = E(max(1 less than or equal to i) (less than or equal to n) Y-i) and V(Y-1,..., Y-n) sup(tauis an element ofC)(n) E(Y-tau), where C-n denotes the set of all stopping rules for Y-1,..., Y-n. Sharp upper bounds for the difference M(Y-1,..., Y-n) -V (Y-1,..., Y-n) are given und...
-
作者：Erhardsson, T
作者单位：Royal Institute of Technology
摘要：Let W be the number of points in (0, t] of a stationary finite-state Markov renewal point process. We derive a bound for the total variation distance between the distribution of W and a compound Poisson distribution. For any nonnegative random variable (, we construct a strong memoryless time zeta such that zeta - t is exponentially distributed conditional on {zeta less than or equal to t, zeta > t}, for each t. This is used to embed the Markov renewal point process into another such process w...
-
作者：Neininger, R; Rüschendorf, L
作者单位：Goethe University Frankfurt; University of Freiburg
摘要：A class of random recursive sequences (Y-n) with slowly varying variances as arising for parameters of random trees or recursive algorithms X leads after normalizations to degenerate limit equations of the form X =(L) X. For nondegenerate limit equations the contraction method is a main tool to establish convergence of the scaled sequence to the unique solution of the limit equation. In this paper we develop an extension of the contraction method which allows us to derive limit theorems for pa...
-
作者：Sabot, C
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite
摘要：We consider random walks in a random environment of the type p(0) + gammaxiz, where p(0) denotes the transition probabilities of a stationary random walk on Z(d), to nearest neighbors, and xi(Z) is an i.i.d. random perturbation. We give an explicit expansion, for small gamma, of the asymptotic speed of the random walk under the annealed law, up to order 2. As an application, we construct, in dimension d greater than or equal to 2, a walk which goes faster than the stationary walk under the mea...
-
作者：Kersting, G; Memisoglu, K
作者单位：Goethe University Frankfurt
摘要：We present two path decompositions of Markov chains (with general state space) by means of harmonic functions, which are dual to each other. They can be seen as a generalization of Williams' decomposition of a Brownian motion with drift. The results may be illustrated by a multitude of examples, but we confine ourselves to different types of random walks and the Polya urn.
-
作者：Liao, M
作者单位：Auburn University System; Auburn University; Nankai University
摘要：We study the Fourier expansion of the distribution density of a Levy process in a compact Lie group based on the Peter-Weyl theorem.
