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We study the problem of scenery reconstruction in arbitrary dimension using observations registered in boxes of size k (for k fixed), seen along a branching random walk. We prove that, using a large enough k for almost all the realizations of the branching random walk, almost all sceneries can be reconstructed up to equivalence. 相似文献
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一类随机环境下随机游动的常返性 总被引:1,自引:0,他引:1
张玥 《纯粹数学与应用数学》2004,20(1):53-56
就一类平稳环境θ下随机流动{Xn}n∈z 建立相应的Markov-双链{ηn}n∈z ={(xn,Tnθ)}n∈z ,并给出在该平稳环境θ下{xn}n∈z 为常返链的条件. 相似文献
4.
We consider linearly edge-reinforced random walk on an arbitrary locally finite connected graph. It is shown that the process
has the same distribution as a mixture of reversible Markov chains, determined by time-independent strictly positive weights
on the edges. Furthermore, we prove bounds for the random weights, uniform, among others, in the size of the graph.
相似文献
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Fixed points of the smoothing transformation 总被引:4,自引:0,他引:4
Summary Let W
1,..., W
N
be N nonnegative random variables and let
be the class of all probability measures on [0, ∞). Define a transformation T on
by letting Tμ be the distribution of W
1X1+ ... + W
N
X
N
, where the X
i
are independent random variables with distribution μ, which are independent of W
1,..., W
N
as well. In earlier work, first Kahane and Peyriere, and then Holley and Liggett, obtained necessary and sufficient conditions
for T to have a nontrivial fixed point of finite mean in the special cases that the W
i
are independent and identically distributed, or are fixed multiples of one random variable. In this paper we study the transformation
in general. Assuming only that for some γ>1, EW
i
γ
<∞ for all i, we determine exactly when T has a nontrivial fixed point (of finite or infinite mean). When it does, we find all fixed points and prove a convergence
result. In particular, it turns out that in the previously considered cases, T always has a nontrivial fixed point. Our results were motivated by a number of open problems in infinite particle systems.
The basic question is: in those cases in which an infinite particle system has no invariant measures of finite mean, does
it have invariant measures of infinite mean? Our results suggest possible answers to this question for the generalized potlatch
and smoothing processes studied by Holley and Liggett.
The research of both authors was supported in part by NSF Grant MCS 80-02732. The first author is an Alfred P. Sloan fellow 相似文献
7.
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
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We consider a branching random walk with a random environment in time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The environment is supposed to be independent and identically distributed. For A ?, let Zn(A) be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn(·) with appropriate normalization. 相似文献
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Consider a time-inhomogeneous branching random walk, generated by the point process Ln which composed by two independent parts: ‘branching’offspring Xn with the mean for and ‘displacement’ with a drift for , where the ‘branching’ process is supercritical for B>0 but ‘asymptotically critical’ and the drift of the ‘displacement’ is strictly positive or negative for but ‘asymptotically’ goes to zero as time goes to infinity. We find that the limit behavior of the minimal (or maximal) position of the branching random walk is sensitive to the ‘asymptotical’ parameter and . 相似文献
10.
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
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《Stochastic Processes and their Applications》2020,130(7):3990-4027
The integer points (sites) of the real line are marked by the positions of a standard random walk with positive integer jumps. We say that the set of marked sites is weakly, moderately or strongly sparse depending on whether the jumps of the random walk are supported by a bounded set, have finite or infinite mean, respectively. Focussing on the case of strong sparsity and assuming additionally that the distribution tail of the jumps is regularly varying at infinity we consider a nearest neighbor random walk on the set of integers having jumps with probability at every nonmarked site, whereas a random drift is imposed at every marked site. We prove new distributional limit theorems for the so defined random walk in a strongly sparse random environment, thereby complementing results obtained recently in Buraczewski et al. (2019) for the case of moderate sparsity and in Matzavinos et al. (2016) for the case of weak sparsity. While the random walk in a strongly sparse random environment exhibits either the diffusive scaling inherent to a simple symmetric random walk or a wide range of subdiffusive scalings, the corresponding limit distributions are non-stable. 相似文献
12.
Martin P. W. Zerner 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2000,36(6):43
We express the asymptotic velocity of random walks in random environment satisfying Kalikow's condition in terms of the Lyapounov exponents which have previously been used in the context of large deviations. 相似文献
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In this article, we mainly discuss the asymptotic behavior for multi-dimensional continuous-time random walk in random environment with holding times. By constructing a renewal structure and using the point “environment viewed from the particle”, under General Kalikow's Condition, we show the law of large numbers (LLN) and central limit theorem (CLT) for the escape speed of random walk. 相似文献
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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
15.
We give a new proof of the central limit theorem for one dimensional symmetric random walk in random environment. The proof
is quite elementary and natural. We show the convergence of the generators and from this we conclude the convergence of the
process. We also investigate the hydrodynamic limit (HDL) of one dimensional symmetric simple exclusion in random environment
and prove stochastic convergence of the scaled density field. The macroscopic behaviour of this field is given by a linear
heat equation. The diffusion coefficient is the same as that of the corresponding random walk.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
16.
There are three parts in this article. In Section 1, we establish the model of branching chain with drift in space-time random environment (BCDSTRE), i.e., the coupling of branching chain and random walk. In Section 2, we prove that any BCDSTRE must be a Markov chain in time random environment when we consider the distribution of the particles in space as a random element. In Section 3, we calculate the first-order moments and the second-order moments of BCDSTRE. 相似文献
17.
LI YingQiu HU YangLi & LIU QuanSheng College of Mathematics Computing Sciences Changsha University of Science Technology Changsha China College of Mathematics Computer Sciences Hunan Normal University Changsha LMAM University of Bretgne-Sud BP Vannes France 《中国科学 数学(英文版)》2011,(7)
Let W be the limit of the normalized population size of a supercritical branching process in a varying or random environment. By an elementary method, we find sufficient conditions under which W has finite weighted moments of the form EWpl(W), where p > 1, l 0 is a concave or slowly varying function. 相似文献
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The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Zd, d≥1. The red particles jump at rate 1 and are in a Poisson equilibrium with density μ. The green particle also jumps at rate 1, but uses different transition kernels p′ and p″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ→∞, the speed of the green particle tends to the average jump under p′. This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. 相似文献