共查询到20条相似文献,搜索用时 15 毫秒
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《Stochastic Processes and their Applications》2001,92(2):181-200
We present a strong approximation of two-dimensional Kesten–Spitzer random walk in random scenery by Brownian motion. 相似文献
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We consider the simple random walk on the (unique) infinite cluster of super-critical bond percolation in ℤ
d
with d≥2. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to that
of non-degenerate, isotropic Brownian motion. Our analysis is based on the consideration of a harmonic deformation of the
infinite cluster on which the random walk becomes a square-integrable martingale. The size of the deformation, expressed by
the so called corrector, is estimated by means of ergodicity arguments. 相似文献
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We consider the simple random walk on random graphs generated by discrete point processes. This random walk moves on graphs whose vertex set is a random subset of a cubic lattice and whose edges are lines between any consecutive vertices on lines parallel to each coordinate axis. Under the assumption that the discrete point processes are finitely dependent and stationary, we prove that the quenched invariance principle holds, i.e., for almost every configuration of the point process, the path distribution of the walk converges weakly to that of a Brownian motion. 相似文献
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Wen Jiwei Yan Yunliang 《高校应用数学学报(英文版)》2006,21(1):87-95
Let X,X1,X2 be i. i. d. random variables with EX^2+δ〈∞ (for some δ〉0). Consider a one dimensional random walk S={Sn}n≥0, starting from S0 =0. Let ζ* (n)=supx∈zζ(x,n),ζ(x,n) =#{0≤k≤n:[Sk]=x}. A strong approximation of ζ(n) by the local time for Wiener process is presented and the limsup type and liminf-type laws of iterated logarithm of the maximum local time ζ*(n) are obtained. Furthermore,the precise asymptoties in the law of iterated logarithm of ζ*(n) is proved. 相似文献
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We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that
the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance principle
and considering environments with an L2 averaged drift. We also state an a.s. invariance principle for random walks in general random environments whose hypothesis
requires a subdiffusive bound on the variance of the quenched mean, under an ergodic invariant measure for the environment
chain.
T. Sepp?l?inen was partially supported by National Science Foundation grant DMS-0402231. 相似文献
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Ernst Eberlein 《Probability Theory and Related Fields》1979,50(2):119-133
Summary It is shown that for -mixing arrays of Banach space valued random vectors the central limit theorem implies the invariance principle. Applying this result to lattices of random variables a higher dimensional invariance principle under dependence assumptions is obtained.Dedicated to Professor Leopold Schmetterer 相似文献
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We investigate in this work the asymptotic behavior of isotropic diffusions in random environment that are small perturbations
of Brownian motion. When the space dimension is three or more, we prove an invariance principle as well as transience. Our
methods also apply to questions of homogenization in random media. 相似文献
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Let ?(n,x) be the local time of a random walk on Z2. We prove a strong law of large numbers for the quantity Ln(α)=∑x∈Z2?(n,x)α for all α≥0. We use this result to describe the distribution of the local time of a typical point in the range of the random walk. 相似文献
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Summary Necessary and sufficient conditions are given for Strassen's invariance principle ([6]) in case a random subsequence is considered.
A few iterated logarithm laws for random subsequences are derived as corollaries. These results generalize, in particular,
those obtained by Chow et al. ([1]). 相似文献
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(ρ)-混合序列的不变原理 总被引:7,自引:1,他引:6
吴群英 《纯粹数学与应用数学》2003,19(1)
给出一类较广泛的(ρ)-混合序列,并证明了在一定的矩条件下,(ρ)-混合序列的不变原理成立. 相似文献