共查询到20条相似文献,搜索用时 171 毫秒
1.
Yuri Kifer 《Transactions of the American Mathematical Society》1998,350(4):1481-1518
I derive general relativized central limit theorems and laws of iterated logarithm for random transformations both via certain mixing assumptions and via the martingale differences approach. The results are applied to Markov chains in random environments, random subshifts of finite type, and random expanding in average transformations where I show that the conditions of the general theorems are satisfied and so the corresponding (fiberwise) central limit theorems and laws of iterated logarithm hold true in these cases. I consider also a continuous time version of such limit theorems for random suspensions which are continuous time random dynamical systems.
2.
C. C. Heyde 《Stochastic Processes and their Applications》1985,20(2):307-314
Let {Xk} be a stationary ergodic sequence of nonnegative matrices. It is shown in this paper that, under mild additional conditions, the logarithm of the i, jth element of Xt···X1 is well approximated by a sum of t random variables from a stationary ergodic sequence. This representation is very useful for the study of limit behaviour of products of random matrices. An iterated logarithm result and an estimation result of use in the theory of demographic population projections are derived as corollaries. 相似文献
3.
We consider a discrete time random environment. We state that when the random walk on real number space in a environment is i.i.d., under the law, the law of large numbers, iterated law and CLT of the process are correct space-time random marginal annealed Using a martingale approach, we also state an a.s. invariance principle for random walks in general random environment whose hypothesis requires a subdiffusive bound on the variance of the quenched mean, under an ergodic invariant measure for the environment chain. 相似文献
4.
Xia Chen 《Journal of Theoretical Probability》2006,19(3):721-739
We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup
and the liminf laws of the iterated logarithm.
We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup
and the liminf laws of the iterated logarithm. 相似文献
5.
Michael Voit 《Journal of Theoretical Probability》1993,6(4):653-669
We derive laws of the iterated logarithm for Markov chains on the nonnegative integers whose transition probabilities are associated with a sequence of orthogonal polynomials. These laws can be applied to a large class of birth and death random walks and random walks on polynomial hypergroups. In particular, the results of our paper lead immediately to a law of the iterated logarithm for the growth of the distance of isotropic random walks on infinite distance-transitive graphs as well as on certain finitely generated semigroups from their starting points. 相似文献
6.
We construct a sequence of transient random walks in random environments and prove that by proper scaling, it converges to a diffusion process with drifted Brownian potential. To this end, we prove a counterpart of convergence for transient random walk in non-random environment, which is interesting itself. 相似文献
7.
A representation for a weakly ergodic sequence of (nonstochastic) matrices allows products of nonnegative matrices which eventually become strictly positive to be expressed via products of some associated stochastic matrices and ratios of values of a certain function. This formula used in a random setup leads to a representation for the logarithm of a random matrix product. If the sequence of random matrices is in addition stationary then automatically almost all sequences are weakly ergodic, and the representation is expressed in terms of an one-dimensional stationary process. This permits properties of products of random matrices to be deduced from the latter. Second moment assumptions guarantee that central limit theorems and laws of the iterated logarithm hold for the random matrix products if and only if they hold for the corresponding stationary process. Finally, a central limit theorem for some classes of weakly dependent stationary random matrices is derived doing away with the restriction of boundedness of the ratios of colum entries assumed by previous studies. Extensions beyond stationarity are discussed. 相似文献
8.
Franois Simenhaus 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2007,43(6):751-761
In this paper we study the existence of an asymptotic direction for random walks in random i.i.d. environments (RWRE). We prove that if the set of directions where the walk is transient contains a non-empty open set, the walk admits an asymptotic direction. The main tool to obtain this result is the construction of a renewal structure with cones. We also prove that RWRE admits at most two opposite asymptotic directions. 相似文献
9.
We consider random walks in a balanced random environment in ${\mathbb{Z}^d}$ , d?≥ 2. We first prove an invariance principle (for d?≥ 2) and the transience of the random walks when d?≥ 3 (recurrence when d?=?2) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for random walks in i.i.d. balanced environments. 相似文献
10.
In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes. 相似文献
11.
研究了在环境平稳遍历时,右半直线上可逗留的随机环境中的随机游动的常返性和非常返性,给出非常返、正常返、零常返的充要条件,并讨论了极限性质.作为推论,给出P独立同分布时的相应结论. 相似文献
12.
13.
Ilya Ya. Goldsheid 《Probability Theory and Related Fields》2008,141(3-4):471-511
The main goal of this work is to study the asymptotic behaviour of hitting times of a random walk (RW) in a quenched random
environment (RE) on a strip. We introduce enlarged random environments in which the traditional hitting time can be presented as a sum of independent random variables whose distribution functions
form a stationary random sequence. This allows us to obtain conditions (stated in terms of properties of random environments)
for a linear growth of hitting times of relevant random walks. In some important cases (e.g. independent random environments)
these conditions are also necessary for this type of behaviour. We also prove the quenched Central Limit Theorem (CLT) for
hitting times in the general ergodic setting. A particular feature of these (ballistic) laws in random environment is that,
whenever they hold under standard normalization, the convergence is a convergence with a speed. The latter is due to certain
properties of moments of hitting times which are also studied in this paper. The asymptotic properties of the position of
the walk are stated but are not proved in this work since this has been done in Goldhseid (Probab. Theory Relat. Fields 139(1):41–64,
2007).
相似文献
14.
We study the path behaviour of general random walks, and that of their local times, on the 2-dimensional comb lattice C2 that is obtained from Z2 by removing all horizontal edges off the x-axis. We prove strong approximation results for such random walks and also for their local times. Concentrating mainly on the latter, we establish strong and weak limit theorems, including Strassen-type laws of the iterated logarithm, Hirsch-type laws, and weak convergence results in terms of functional convergence in distribution. 相似文献
15.
《Stochastic Processes and their Applications》2019,129(11):4239-4268
We prove that loop-erased random walks on the finite pre-Sierpiński gaskets can be extended to a loop-erased random walk on the infinite pre-Sierpiński gasket by using the ‘erasing-larger-loops-first’ method, and obtain the asymptotic behavior of the walk as the number of steps increases, in particular, the displacement exponent and a law of the iterated logarithm. 相似文献
16.
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
17.
In this article,we obtain the central limit theorem and the law of the iterated logarithm for Galton-Watson processes in i.i.d.random environments. 相似文献
18.
Ilya Ya. Goldsheid 《Probability Theory and Related Fields》2007,139(1-2):41-64
We consider a simple random walk (dimension one, nearest neighbour jumps) in a quenched random environment. The goal of this
work is to provide sufficient conditions, stated in terms of properties of the environment, under which the central limit
theorem (CLT) holds for the position of the walk. Verifying these conditions leads to a complete solution of the problem in
the case of independent identically distributed environments as well as in the case of uniformly ergodic (and thus also weakly
mixing) environments.
相似文献
19.
Mei Juan Zhang 《数学学报(英文版)》2014,30(3):395-410
We consider a random walk in random environment on a strip, which is transient to the right. The random environment is stationary and ergodic. By the constructed enlarged random environment which was first introduced by Goldsheid (2008), we obtain the large deviations conditioned on the environment (in the quenched case) for the hitting times of the random walk. 相似文献
20.
We introduce the directed-edge-reinforced random walk and prove that the process is equivalent to a random walk in random
environment. Using Oseledec"s multiplicative ergodic theorem, we obtain recurrence and transience criteria for random walks
in random environment on graphs with a certain linear structure and apply them to directed-edge-reinforced random walks.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献