-
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.
-
作者：Bai, ZD; Silverstein, JW
作者单位：Northeast Normal University - China; North Carolina State University; National University of Singapore
摘要：Let B-n = (1/N)T-n(1/2) XnX*T-n(n)1/2 where X-n = (X-ij) is n x N with i.i.d. complex standardized entries having finite fourth moment, and T-n(1/2) is a Hermitian square root of the nonnegative definite Hermitian matrix T-n. The limiting behavior, as n --> infinity with n/N approaching a positive constant, of functionals of the eigenvalues of B-n, where each is given equal weight, is studied. Due to the limiting behavior of the empirical spectral distribution of B,,, it is known that these li...
-
作者：Jacod, J
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study the Euler scheme for a stochastic differential equation driven by a Levy process Y. More precisely, we look at the asymptotic behavior of the normalized error process u(n) (X-n - X), where X is the true solution and X-n is its Euler approximation with stepsize 1/n, and u(n) is an appropriate rate going to infinity: if the normalized error processes converge, or are at least tight, we say that the sequence (u(n)) is a rate, which, in addition, is sharp when the limiting process (or pro...
-
作者：Einmahl, U; Kuelbs, J
作者单位：Universite Libre de Bruxelles; University of Wisconsin System; University of Wisconsin Madison
摘要：Precise asymptotics for moderate deviation probabilities are established for open convex sets in both the finite- and infinite-dimensional settings. Our results are based on the existence of dominating points for these sets, a related representation formula, and asymptotics for the integral term in this formula.
-
作者：Abadi, M
作者单位：Universidade de Sao Paulo
摘要：We prove an upper bound for the error in the exponential approximation of the hitting time law of a rare event in alpha-mixing processes with exponential decay, phi-mixing processes with a summable function phi and for general psi-mixing processes with a finite alphabet. In the first case the bound is uniform as a function of the measure of the event. In the last two cases the bound depends also on the time scale t. This allows us to get further statistical properties as the ratio convergence ...
-
作者：Chistyakov, GP; Götze, F
作者单位：National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine; University of Bielefeld
摘要：Let X, X-j, j is an element of N, be independent, identically distributed random variables with probability distribution F. It is shown that Student's statistic of the sample {X-j}(n)(j=1), has a limit distribution G such that G({-1, 1}) not equal 1, if and only if: (1) X is in the domain of attraction of a stable law with some exponent 0 < alpha less than or equal to 2; (2) EX = 0 if 1 < alpha < 2; (3) if alpha = 1, then X is in the domain of attraction of Cauchy's law and Feller's condition ...
