共查询到20条相似文献,搜索用时 15 毫秒
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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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Acta Mathematica Hungarica - 相似文献
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André Dabrowski Herold Dehling Walter Philipp 《Probability Theory and Related Fields》1984,65(4):483-491
Summary We give a simpler proof of the probability invariance principle for triangular arrays of independent identically distributed random variables with values in a separable Banach space, recently proved by de Acosta [1], and improve this result to an almost sure invariance principle. 相似文献
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Erich Berger 《Probability Theory and Related Fields》1990,84(2):161-201
Summary In this paper we establish an almost sure invariance principle with an error termo((t log logt)1/2) (ast) for partial sums of stationary ergodic martingale difference sequences taking values in a real separable Banach space. As partial sums of weakly dependent random variables can often be well approximated by martingales, this result also leads to almost sure invariance principles for a wide class of stationary ergodic sequences such as ø-mixing and -mixing sequences and functionals of such sequences. Compared with previous related work for vector valued random variables (starting with an article by Kuelbs and Philipp [27]), the present approach leads to a unification of the theory (at least for stationary sequences), moment conditions required by earlier authors are relaxed (only second order weak moments are needed), and our proofs are easier in that we do not employ estimates of the rate of convergence in the central limit theorem but merely the central limit theorem itself. 相似文献
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U. Einmahl 《Journal of Mathematical Sciences》2009,163(4):311-327
We provide a strong invariance principle for sums of independent, identically distributed random vectors that need not have
finite second absolute moments. Various applications are indicated. In particular, we show how one can re-obtain some recent
LIL type results from this invariance principle. Bibliography: 16 titles. 相似文献
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Michael A. Kouritzin 《Journal of Theoretical Probability》1996,9(4):811-840
Since the novel work of Berkes and Philipp(3) much effort has been focused on establishing almost sure invariance principles of the form (1) $$\left| {\sum\limits_{i = 1}^{|\_t\_|} {x_1 - X_t } } \right| \ll t^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2} - \gamma } $$ where {x i ,i=1,2,3,...} is a sequence of random vectors and {X t ,t>-0} is a Brownian motion. In this note, we show that if {A k ,k=1,2,3,...} and {b k ,k=1,2,3,...} are processes satisfying almost-sure bounds analogous to Eq. (1), (where {X t ,t≥0} could be a more general Gauss-Markov process) then {h k ,k=1,2,3...}, the solution of the stochastic approximation or adaptive filtering algorithm (2) $$h_{k + 1} = h_k + \frac{1}{k}(b_k - A_k h_k )for{\text{ }}k{\text{ = 1,2,3}}...$$ also satisfies and almost sure invariance principle of the same type. 相似文献
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We study necessary and sufficient conditions for the almost sure convergence of averages of independent random variables with multidimensional indices obtained by certain summability methods. 相似文献
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Let X, X1 , X2 , ··· be a sequence of nondegenerate i.i.d. random variables with zero means, which is in the domain of attraction of the normal law. Let {a ni , 1≤i≤n, n≥1} be an array of real numbers with some suitable conditions. In this paper, we show that a central limit theorem for self-normalized weighted sums holds. We also deduce a version of ASCLT for self-normalized weighted sums. 相似文献
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Le Van Thanh 《Acta Mathematica Hungarica》2013,139(3):276-285
This work develops almost sure convergence of negatively associated random vectors in Hilbert spaces. Extensions of a result in [4] are given. Illustrative examples are provided. 相似文献
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Complete convergence and almost sure convergence of weighted sums of random variables 总被引:6,自引:0,他引:6
Deli Li M. Bhaskara Rao Tiefeng Jiang Xiangchen Wang 《Journal of Theoretical Probability》1995,8(1):49-76
Letr>1. For eachn1, let {X
nk
, –<k<} be a sequence of independent real random variables. We provide some very relaxed conditions which will guarantee
for every >0. This result is used to establish some results on complete convergence for weighted sums of independent random variables. The main idea is that we devise an effetive way of combining a certain maximal inequality of Hoffmann-Jørgensen and rates of convergence in the Weak Law of Large Numbers to establish results on complete convergence of weighted sums of independent random variables. New results as well as simple new proofs of known ones illustrate the usefulness of our method in this context. We show further that this approach can be used in the study of almost sure convergence for weighted sums of independent random variables. Convergence rates in the almost sure convergence of some summability methods ofiid random variables are also established. 相似文献
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Yong Zhang Xiao-Yun Yang Zhi-Shan Dong 《Journal of Mathematical Analysis and Applications》2009,355(2):708-41
Let be a strictly stationary positively or negatively associated sequence of positive random variables with EX1=μ>0, and VarX1=σ2<∞. Denote , and γ=σ/μ the coefficient of variation. Under suitable conditions, we show that
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In this paper we prove an almost sure limit theorem for random sums of independent random variables in the domain of attraction
of a p-semistable law and describe the limit law. 相似文献
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Pter Major 《Journal of multivariate analysis》1978,8(4):487-517
The paper deals with the invariance principle for sums of independent identically distributed random variables. First it compares the different possibilities of posing the problem. The sharpest results of this theory are presented with a sketch of their proofs. At the end of the paper some unsolved problems are given. 相似文献
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Christophe Dupont 《Probability Theory and Related Fields》2010,146(3-4):337-359
Let f be an holomorphic endomorphism of ${\mathbb{P}^k}$ and μ be its measure of maximal entropy. We prove an almost sure invariance principle for the systems ${(\mathbb{P}^k,f,\mu)}$ . Our class ${\mathcal {U}}$ of observables includes the Hölder functions and unbounded ones which present analytic singularities. The proof is based on a geometric construction of a Bernoulli coding map ${\omega: (\Sigma, s, \nu) \to (\mathbb{P}^k,f,\mu)}$ . We obtain the invariance principle for an observable ψ on ${(\mathbb{P}^k,f,\mu)}$ by applying Philipp–Stout’s theorem for ${\chi = \psi \circ \omega}$ on (Σ, s, ν). The invariance principle implies the central limit theorem as well as several statistical properties for the class ${\mathcal {U}}$ . As an application, we give a direct proof of the absolute continuity of the measure μ when it satisfies Pesin’s formula. This approach relies on the central limit theorem for the unbounded observable log ${{\tt Jac}\, f \in \mathcal{U}}$ . 相似文献
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Wen Sheng Wang 《数学学报(英文版)》2014,30(9):1555-1565
Let θ∈ Rdbe a unit vector and let X,X1,X2,...be a sequence of i.i.d.Rd-valued random vectors attracted to operator semi-stable laws.For each integer n ≥ 1,let X1,n ≤···≤ Xn,n denote the order statistics of X1,X2,...,Xn according to priority of index,namely | X1,n,θ | ≥···≥ | Xn,n,θ |,where ·,· is an inner product on Rd.For all integers r ≥ 0,define by(r)Sn = n-ri=1Xi,n the trimmed sum.In this paper we investigate a law of the iterated logarithm and limit distributions for trimmed sums(r)Sn.Our results give information about the maximal growth rate of sample paths for partial sums of X when r extreme terms are excluded.A stochastically compactness of(r)Sn is obtained. 相似文献