共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
Hua Ming Wang 《数学学报(英文版)》2013,29(6):1095-1110
In this paper, we study the total number of progeny, W, before regenerating of multitype branching process with immigration in random environment. We show that the tail probability of |W| is of order t-κ as t→∞, with κ some constant. As an application, we prove a stable law for (L-1) random walk in random environment, generalizing the stable law for the nearest random walk in random environment (see "Kesten, Kozlov, Spitzer: A limit law for random walk in a random environment. Compositio Math., 30, 145-168 (1975)"). 相似文献
3.
Alain-Sol Sznitman 《Probability Theory and Related Fields》2002,122(4):509-544
We investigate multi-dimensional random walks in random environment. Specifically, we provide an effective criterion which
can be checked by inspection of the environment in a finite box, and implies a ballistic strong law of large numbers, a central
limit theorem and several large deviation controls. With the help of this criterion, we provide an example of a ballistic
multi-dimensional walk which does not fulfill the criterion introduced by Kalikow in [4]. The present work complements the
results of [9], where a certain condition (T) was introduced, and confirms the interest of this condition.
Received: 5 October 2000/ Revised version: 24 May 2001 Published online: 22 February 2002 相似文献
4.
《Stochastic Processes and their Applications》2020,130(2):962-999
We focus on recurrent random walks in random environment (RWRE) on Galton–Watson trees. The range of these walks, that is the number of sites visited at some fixed time, has been studied in three different papers Andreoletti and Chen (2018), Aïdékon and de Raphélis (2017) and de Raphélis (2016). Here we study the heavy range: the number of edges frequently visited by the walk. The asymptotic behavior of this process when the number of visits is a power of the number of steps of the walk is given for all recurrent cases. It turns out that this heavy range plays a crucial role in the rate of convergence of an estimator of the environment from a single trajectory of the RWRE. 相似文献
5.
Wojciech Jaworski 《Journal d'Analyse Mathématique》1998,74(1):235-273
We prove that, given an arbitrary spread out probability measure μ on an almost connected locally compact second countable
groupG, there exists a homogeneous spaceG/H, called the μ-boundary, such that the space of bounded μ-harmonic functions can be identified withL
∞
(G/H). The μ-boundary is an amenable contractive homogeneous space. We also establish that the canonical projection onto the μ-boundary
of the right random walk of law μ always converges in probability and, whenG is amenable, it converges almost surely. The μ-boundary can be characterised as the largest homogeneous space among those
homogeneous spaces in which the canonical projection of the random walk converges in probability. 相似文献
6.
We present a multiscale analysis for the exit measures from large balls in , of random walks in certain i.i.d. random environments which are small perturbations of the fixed environment corresponding
to simple random walk. Our main assumption is an isotropy assumption on the law of the environment, introduced by Bricmont
and Kupiainen. Under this assumption, we prove that the exit measure of the random walk in a random environment from a large
ball, approaches the exit measure of a simple random walk from the same ball, in the sense that the variational distance between
smoothed versions of these measures converges to zero. We also prove the transience of the random walk in random environment.
The analysis is based on propagating estimates on the variational distance between the exit measure of the random walk in
random environment and that of simple random walk, in addition to estimates on the variational distance between smoothed versions
of these quantities.
Partially supported by NSF grant DMS-0503775. 相似文献
7.
Sergey G. Foss Anatolii A. Puhalskii 《Stochastic Processes and their Applications》2011,121(2):288-313
We consider a random walk with a negative drift and with a jump distribution which under Cramér’s change of measure belongs to the domain of attraction of a spectrally positive stable law. If conditioned to reach a high level and suitably scaled, this random walk converges in law to a nondecreasing Markov process which can be interpreted as a spectrally positive Lévy process conditioned not to overshoot level 1. 相似文献
8.
Alain-Sol Sznitman 《Probability Theory and Related Fields》1999,115(3):287-323
We consider a d-dimensional random walk in random environment for which transition probabilities at each site are either neutral or present
an effective drift “pointing to the right”. We obtain large deviation estimates on the probability that the walk moves in
a too slow ballistic fashion, both under the annealed and quenched measures. These estimates underline the key role of large
neutral pockets of the medium in the occurrence of slowdowns of the walk.
Received: 12 March 1998 / Revised version: 19 February 1999 相似文献
9.
Veraverbeke’s (Stoch Proc Appl 5:27–37, 1977) theorem relates the tail of the distribution of the supremum of a random walk with negative drift to the tail of the distribution
of its increments, or equivalently, the probability that a centered random walk with heavy-tail increments hits a moving linear
boundary. We study similar problems for more general processes. In particular, we derive an analogue of Veraverbeke’s theorem
for fractional integrated ARMA models without prehistoric influence, when the innovations have regularly varying tails. Furthermore,
we prove some limit theorems for the trajectory of the process, conditionally on a large maximum. Those results are obtained
by using a general scheme of proof which we present in some detail and should be of value in other related problems. 相似文献
10.
Remco van der Hofstad Frank den Hollander Wolfgang König 《Probability Theory and Related Fields》2003,125(4):483-521
In this paper we present a new and flexible method to show that, in one dimension, various self-repellent random walks converge
to self-repellent Brownian motion in the limit of weak interaction after appropriate space-time scaling. Our method is based
on cutting the path into pieces of an appropriately scaled length, controlling the interaction between the different pieces,
and applying an invariance principle to the single pieces. In this way, we show that the self-repellent random walk large
deviation rate function for the empirical drift of the path converges to the self-repellent Brownian motion large deviation
rate function after appropriate scaling with the interaction parameters. The method is considerably simpler than the approach
followed in our earlier work, which was based on functional analytic arguments applied to variational representations and
only worked in a very limited number of situations.
We consider two examples of a weak interaction limit: (1) vanishing self-repellence, (2) diverging step variance. In example
(1), we recover our earlier scaling results for simple random walk with vanishing self-repellence and show how these can be
extended to random walk with steps that have zero mean and a finite exponential moment. Moreover, we show that these scaling
results are stable against adding self-attraction, provided the self-repellence dominates. In example (2), we prove a conjecture
by Aldous for the scaling of self-avoiding walk with diverging step variance. Moreover, we consider self-avoiding walk on
a two-dimensional horizontal strip such that the steps in the vertical direction are uniform over the width of the strip and
find the scaling as the width tends to infinity.
Received: 6 March 2002 / Revised version: 11 October 2002 / Published online: 21 February 2003
Mathematics Subject Classification (2000): 60F05, 60F10, 60J55, 82D60
Key words or phrases: Self-repellent random walk and Brownian motion – Invariance principles – Large deviations – Scaling limits – Universality 相似文献
11.
We construct the Poisson boundary for a random walk supported by the general linear group on the rational numbers as the product
of flag manifolds over the p-adic fields. For this purpose, we prove a law of large numbers using Oseledets’ multiplicative ergodic theorem. The only
assumption we need is some moment condition on the measure governing the jumps of the random walk, but no irreducibility hypothesis
is made. 相似文献
12.
E. B. Yarovaya 《Moscow University Mathematics Bulletin》2010,65(2):78-80
The paper discusses two models of a branching random walk on a many-dimensional lattice with birth and death of particles
at a single node being the source of branching. The random walk in the first model is assumed to be symmetric. In the second
model an additional parameter is introduced which enables “artificial” intensification of the prevalence of branching or walk
at the source and, as the result, violating the symmetry of the random walk. The monotonicity of the return probability into
the source is proved for the second model, which is a key property in the analysis of branching random walks. 相似文献
13.
Hua-Ming Wang 《Journal of Theoretical Probability》2018,31(2):619-642
We study a random walk with unbounded jumps in random environment. The environment is stationary and ergodic, uniformly elliptic and decays polynomially with speed \(Dj^{-(3+\varepsilon _0)}\) for some \(D>0\) and small \(\varepsilon _0>0.\) We prove a law of large numbers under the condition that the annealed mean of the hitting time of the lattice of the positive half line is finite. As the second part, we consider a birth and death process with bounded jumps in stationary and ergodic environment whose skeleton process is a random walk with unbounded jumps in random environment. Under a uniform ellipticity condition, we prove a law of large numbers and give the explicit formula of its velocity. 相似文献
14.
Ostap Hryniv Mikhail V. Menshikov Andrew R. Wade 《Proceedings of the Steklov Institute of Mathematics》2013,282(1):106-123
We study a random walk in random environment on ?+. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i) points endowed with probabilities drawn from a symmetric distribution with heavy tails at 0 and 1, and (ii) “fast points” with a fixed systematic drift. Without these fast points, the model is related to the diffusion in heavy-tailed (“stable”) random potential studied by Schumacher and Singh; the fast points perturb that model. The two components compete to determine the behaviour of the random walk; we identify phase transitions in terms of the model parameters. We give conditions for recurrence and transience and prove almost sure bounds for the trajectories of the walk. 相似文献
15.
Zhou Xianyin 《数学年刊B辑(英文版)》1995,16(1):131-138
ONTHERANGEOFRANDOMWALKSINRANDOMENVIRONMENT¥ZHOUXIANYIN(DepartmentofMathematics,BeijingNormalUniversity,Beijing100875,China.Pr... 相似文献
16.
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
17.
We show that an i.i.d. uniformly colored scenery on ℤ observed along a random walk path with bounded jumps can still be reconstructed
if there are some errors in the observations. We assume the random walk is recurrent and can reach every point with positive
probability. At time k, the random walker observes the color at her present location with probability 1−δ and an error Y
k
with probability δ. The errors Y
k
, k≥0, are assumed to be stationary and ergodic and independent of scenery and random walk. If the number of colors is strictly
larger than the number of possible jumps for the random walk and δ is sufficiently small, then almost all sceneries can be
almost surely reconstructed up to translations and reflections.
Received: 3 February 2002 / Revised version: 15 January 2003 Published online: 28 March 2003
Mathematics Subject Classification (2000): 60K37, 60G50
Key words or phrases:Scenery reconstruction – Random walk – Coin tossing problems 相似文献
18.
Fredrik Johansson Viklund 《Arkiv f?r Matematik》2012,50(2):331-357
We use the known convergence of loop-erased random walk to radial SLE(2) to give a new proof that the scaling limit of loop-erased random walk excursion in the upper half-plane is chordal SLE(2). Our proof relies on a version of Wilson’s algorithm for weighted graphs which is used together with a Beurling-type estimate for random walk excursion. We also establish and use the convergence of the radial SLE path to the chordal SLE path as the bulk point tends to a boundary point. In the final section we sketch how to extend our results to more general simply connected domains. 相似文献
19.
V. I. Lotov 《Siberian Mathematical Journal》2016,57(1):86-92
We obtain asymptotic expansions for the expectation of the first exit time from an expanding strip for a random walk trajectory. We suppose that the distribution of random walk jumps satisfies the Cramér condition on the existence of an exponential moment. 相似文献
20.
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