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作者：Shields, PC
作者单位：University System of Ohio; University of Toledo
摘要：It is known that the length L(x(1)(n)) of the longest block appearing at least twice in a randomly chosen sample path of length it drawn from an i.i.d. process is asymptotically almost surely equal to C log n, where the constant C depends on the process. A simple coding argument will be used to show that for a class of processes called the finite energy processes, L(x(1)(n)) is almost surely upper bounded by C log n, where C is a constant. While the coding technique does not yield the exact co...
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作者：Benaïm, M
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We discuss and disprove a conjecture of Pemantle concerning vertex-reinforced random walks. The setting is a general theory of non-Markovian discrete-time random processes on a finite space E = {1,...,d}, for which the transition probabilities at each step are influenced by the proportion of times each state has been visited. It is shown that, under mild conditions, the asymptotic behavior of the empirical occupation measure of the process is precisely related to the asymptotic behavior of som...
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作者：Bramson, M; Cox, JT; Greven, A
作者单位：University of Wisconsin System; University of Wisconsin Madison; Syracuse University; University of Erlangen Nuremberg
摘要：We consider two critical spatial branching processes on R-d: critical branching Brownian motion, and the critical Dawson-Watanabe process. A basic feature of these processes is that their ergodic behavior is highly dimension dependent. It is known that in low dimensions, d less than or equal to 2, the only invariant measure is delta(0), the unit point mass on the empty state. In high dimensions, d greater than or equal to 3, there is a family {nu(0), theta is an element of [0, infinity)} of ex...
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作者：Graham, C; Méléard, S
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Sorbonne Universite
摘要：We specify the Markov process corresponding to a generalized mollified Boltzmann equation with general motion between collisions and nonlinear bounded jump (collision) operator, and give the nonlinear martingale problem it solves. We consider various Linear interacting particle systems in order to approximate this nonlinear process. We prove propagation of chaos, in variation norm on path space with a precise rate of convergence, using coupling and interaction graph techniques and a representa...
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作者：Liggett, TM
作者单位：University of California System; University of California Los Angeles
摘要：Interacting particle systems is by now a mature area of probability theory, but one that is still very active. We begin this paper by explaining how models from this area arise in fields such as physics and biology. We turn then to a discussion of both older and more recent results about them, concentrating on contact processes, voter models, and exclusion processes. These processes are among the most studied in the field, and have the virtue of relative simplicity in their description, which ...
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作者：Fitzsimmons, PJ
作者单位：University of California System; University of California San Diego
摘要：Let X and Y be symmetric diffusion processes with a common state space, and let P-m (resp. Q(mu)) be the law of X (resp. Y) with its symmetry measure m (resp. mu) as initial distribution. We study the consequences of the absolute continuity condition Q(mu) much less than loc P-m. We show that under this condition there is a smooth version rho of the Radon-Nikodym derivative d(mu)/dm such that 1/2[log rho(X-t) - log rho(X-0)] = M-t + N-t, t < sigma, where M is a continuous local martingale addi...
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作者：Peligrad, M; Utev, S
作者单位：University System of Ohio; University of Cincinnati; La Trobe University; Russian Academy of Sciences
摘要：In this paper we study the CLT for partial sums of a generalized linear process X-n = Sigma(i=1)(n) a(ni)xi(i), where sup(n) Sigma(i=1)(n) a(ni)(2) < infinity, max(1 less than or equal to i less than or equal to n)\a(ni)\ --> 0 as n --> infinity and xi(i)'s are in turn, pairwise mixing martingale differences, mixing sequences or associated sequences. The results are important in analyzing the asymptotical properties of some estimators as well as of linear processes.
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作者：Voit, M
作者单位：Eberhard Karls University of Tubingen
摘要：In this paper we prove central limit theorems of the following kind: let S-d subset of Rd+1 be the unit sphere of dimension d greater than or equal to 2 with uniform distribution omega(d). For each k is an element of N, consider the isotropic random walk (X-n(k))(n greater than or equal to 0) on S-d starting at th north pole with jumps of fixed sizes angle(X-n(k), X-n-1(k)) = pi/root k for all n greater than or equal to 1. Then there is some k(0)(d) such that for all k greater than or equal to...
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作者：Bai, ZD
作者单位：National Sun Yat Sen University
摘要：It was conjectured in the early 1950's that the empirical spectral distribution of an n x n matrix, of lid entries, normalized by a factor of 1/root n, converges to the uniform distribution over the unit disc on the complex plane, which is called the circular law. Only a special case of the conjecture, where the entries of the matrix are standard complex Gaussian, is known. In this paper, this conjecture is proved under the existence of the sixth moment and some smoothness conditions. Some ext...
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作者：Biggins, JD; Kyprianou, AE
作者单位：University of Sheffield
摘要：In the discrete-time supercritical branching random walk, there is a Kesten-Stigum type result for the martingales formed by the Laplace transform of the nth generation positions. Roughly, this says that for suitable values of the argument of the Laplace transform the martingales converge in mean provided an X log X condition holds. Here it is established that when this moment condition fails, so that the martingale converges to zero, it is possible to find a (Seneta-Heyde) renormalization of ...
