共查询到20条相似文献,搜索用时 15 毫秒
1.
Alexander Bendikov Wojciech Cygan Bartosz Trojan 《Stochastic Processes and their Applications》2017,127(10):3268-3290
We consider a random walk which is obtained from the simple random walk by a discrete time version of Bochner’s subordination. We prove that under certain conditions on the subordinator appropriately scaled random walk converges in the Skorohod space to the symmetric -stable process . We also prove asymptotic formula for the transition function of similar to the Pólya’s asymptotic formula for . 相似文献
2.
Michael Lin Ben-Zion Rubshtein Rainer Wittmann 《Probability Theory and Related Fields》1994,100(3):285-300
Let be an ergodic and conservative non-singular transformation of (, ,m) (thedynamic environment), let
w
be a random probability on a locally compact second countable groupG, and define
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We study the random walk in a random environment on Z+={0,1,2,…}, where the environment is subject to a vanishing (random) perturbation. The two particular cases that we consider are: (i) a random walk in a random environment perturbed from Sinai’s regime; (ii) a simple random walk with a random perturbation. We give almost sure results on how far the random walker is from the origin, for almost every environment. We give both upper and lower almost sure bounds. These bounds are of order (logt)β, for β∈(1,∞), depending on the perturbation. In addition, in the ergodic cases, we give results on the rate of decay of the stationary distribution. 相似文献
5.
We study continuous-time (variable speed) random walks in random environments on , , where, at time t, the walk at x jumps across edge at time-dependent rate . The rates, which we assume stationary and ergodic with respect to space–time shifts, are symmetric and bounded but possibly degenerate in the sense that the total jump rate from a vertex may vanish over finite intervals of time. We formulate conditions on the environment under which the law of diffusively-scaled random walk path tends to Brownian motion for almost every sample of the rates. The proofs invoke Moser iteration to prove sublinearity of the corrector in pointwise sense; a key additional input is a conversion of certain weighted energy norms to ordinary ones. Our conclusions apply to random walks on dynamical bond percolation and interacting particle systems as well as to random walks arising from the Helffer–Sjöstrand representation of gradient models with certain non-strictly convex potentials. 相似文献
6.
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.
7.
Andrea Collevecchio 《Probability Theory and Related Fields》2006,136(1):81-101
Consider a linearly edge-reinforced random walk defined on the b-ary tree, b≥70. We prove the strong law of large numbers for the distance of this process from the root. We give a sufficient condition
for this strong law to hold for general edge-reinforced random walks and random walks in a random environment. We also provide
a central limit theorem.
Supported in part by a Purdue Research Foundation fellowship
this work is part of the author's PhD thesis. 相似文献
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Yuqiang LI 《Frontiers of Mathematics in China》2013,8(2):371-391
We study the functional limits of continuous-time random walks (CTRWs) with tails under certain conditions. We find that the scaled CTRWs with tails converge weakly to an α-stable Lévy process in D([0, 1]) with M 1-topology but the corresponding scaled CTRWs converge weakly to the same limit in D([0, 1]) with J 1-topology. 相似文献
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Harry Kesten 《Journal d'Analyse Mathématique》1963,11(1):323-379
14.
V. V. Chichagov 《Journal of Mathematical Sciences》1995,75(1):1461-1468
The limit behavior of Markov chains with discrete time and a finite number of states (MCDT) depending on the number n of its
steps has been almost completely investigated [1–4]. In [5], MCDT with forbidden transitions were investigated, and in [6],
the sum of a random number of functionals of random variables related by a homogeneous Markov chain (HMC) was considered.
In the present paper, we continue the investigation of the limit behavior of the MCDT with random stopping time which is determined
by a Markov walk plan II with a fixed number of certain transitions [7, 8]. Here we apply a method similar to that of [6],
which allows us to obtain, together with some generalizations of the results of [6], a number of new assertions.
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 119–130, Perm, 1990. 相似文献
15.
Summary LetX be a diffusion in natural scale on (0,1], with 1 reflecting, and letc(x)(H
x
) andv(x)var (H
x
), whereH
x
=inf{t: X
t
=x}. Let
x
=sup{t:X
t
=x}. The main results of this paper are firstly that (i)c is slowly varying; (ii)
are all equivalent: and secondly that (v)
are all equivalent, and are implied by the condition
. Other partial results for more general limit theorems are proved, and new results on regular variation are established. 相似文献
16.
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
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