共查询到9条相似文献,搜索用时 15 毫秒
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Irene Crimaldi Paolo Dai Pra Pierre-Yves Louis Ida G. Minelli 《Stochastic Processes and their Applications》2019,129(1):70-101
We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks. Due to a reinforcement mechanism and interaction, the walks are strongly correlated and converge almost surely to the same, possibly random, limit. We study random walks interacting through a mean-field rule and compare the rate they converge to their limit with the rate of synchronization, i.e. the rate at which their mutual distances converge to zero. We show that, under certain conditions, synchronization is faster than convergence. Even if our focus is on theoretical results, we propose as main motivations two contexts in which such results could directly apply: urn models and opinion dynamics in a random network evolving via preferential attachment. 相似文献
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Eric David Belsley 《Probability Theory and Related Fields》1998,112(4):493-533
When run on any non-bipartite q-distance regular graph from a family containing graphs of arbitrarily large diameter d, we show that d steps are necessary and sufficient to drive simple random walk to the uniform distribution in total variation distance, and
that a sharp cutoff phenomenon occurs. For most examples, we determine the set on which the variation distance is achieved,
and the precise rate at which it decays.
The upper bound argument uses spectral methods – combining the usual Cauchy-Schwarz bound on variation distance with a bound
on the tail probability of a first-hitting time, derived from its generating function.
Received: 2 April 1997 / Revised version: 10 May 1998 相似文献
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A second order asymptotic expansion in the local limit theorem for a simple branching random walk in
Zhi-Qiang Gao 《Stochastic Processes and their Applications》2018,128(12):4000-4017
Consider a branching random walk, where the underlying branching mechanism is governed by a Galton–Watson process and the migration of particles by a simple random walk in . Denote by the number of particles of generation located at site . We give the second order asymptotic expansion for . The higher order expansion can be derived by using our method here. As a by-product, we give the second order expansion for a simple random walk on , which is used in the proof of the main theorem and is of independent interest. 相似文献
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Liviu I. Nicolaescu 《Stochastic Processes and their Applications》2017,127(10):3412-3446
We prove a central limit theorem concerning the number of critical points in large cubes of an isotropic Gaussian random function on a Euclidean space. 相似文献
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高志强 《数学物理学报(B辑英文版)》2018,38(4):1259-1268
Consider a branching random walk, where the underlying branching mechanism is governed by a Galton-Watson process and the moving law of particles by a discrete random variable on the integer lattice Z. Denote by Z_n(z) the number of particles in the n-th generation in the model for each z ∈ Z. We derive the exact convergence rate in the local limit theorem for Z_n(z) assuming a condition like "EN(log N)~(1+λ) ∞" for the offspring distribution and a finite moment condition on the motion law. This complements the known results for the strongly non-lattice branching random walk on the real line and for the simple symmetric branching random walk on the integer lattice. 相似文献
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Carsten Chong Claudia Klüppelberg 《Stochastic Processes and their Applications》2019,129(12):4998-5036
We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To capture these effects, we define a partial mean field system, and prove a law of large numbers with explicit bounds on the mean squared error. Furthermore, a large deviation result is established under reasonable assumptions. The theory will be illustrated by several examples: on the one hand, we recover the classical results of chaos propagation for homogeneous systems, and on the other hand, we demonstrate the validity of our assumptions for quite general heterogeneous networks including those arising from preferential attachment random graph models. 相似文献
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Multivariate Bessel processes describe the stochastic dynamics of interacting particle systems of Calogero–Moser–Sutherland type and are related with -Hermite and Laguerre ensembles. It was shown by Andraus, Katori, and Miyashita that for fixed starting points, these processes admit interesting limit laws when the multiplicities tend to , where in some cases the limits are described by the zeros of classical Hermite and Laguerre polynomials. In this paper we use SDEs to derive corresponding limit laws for starting points of the form for with in the interior of the corresponding Weyl chambers. Our limit results are a.s. locally uniform in time. Moreover, in some cases we present associated central limit theorems. 相似文献