共查询到20条相似文献,搜索用时 15 毫秒
1.
Richard Durrett 《Stochastic Processes and their Applications》1979,9(2):117-135
In recent years several authors have obtained limit theorems for the location of the right most particle in a supercritical branching random walk. In this paper we will consider analogous problems for an exponentially growing number of independent random walks. A comparison of our results with the known results of branching random walk then identifies the limit behaviors which are due to the number of particles and those which are determined by the branching structure. 相似文献
2.
A tanglegram consists of two binary rooted trees with the same number of leaves and a perfect matching between the leaves of the trees. We show that the two halves of a random tanglegram essentially look like two independently chosen random plane binary trees. This fact is used to derive a number of results on the shape of random tanglegrams, including theorems on the number of cherries and generally occurrences of subtrees, the root branches, the number of automorphisms, and the height. For each of these, we obtain limiting probabilities or distributions. Finally, we investigate the number of matched cherries, for which the limiting distribution is identified as well. 相似文献
3.
We prove some heavy-traffic limit theorems for processes which encompass the fractionally integrated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a non-Gaussian stable distribution. 相似文献
4.
Vygantas Paulauskas 《Journal of multivariate analysis》2010,101(3):621-639
We consider linear random fields and show how an analogue of the Beveridge-Nelson decomposition can be applied to prove limit theorems for sums of such fields. 相似文献
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We prove some heavy-traffic limit theorems for some nonstationary linear processes which encompass the fractionally differentiated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a non-Gaussian stable distribution. The results are based on an extension of the point process methodology to linear processes with nonsummable coefficients and make use of a new maximal type inequality. 相似文献
7.
M. Gordin 《Journal of Mathematical Sciences》2009,163(4):363-374
It is known that under some conditions, a stationary random sequence admits a representation as a sum of two sequences: one
of them is a martingale difference sequence, and another one is a so-called coboundary. Such a representation can be used
for proving some limit theorems by means of the martingale approximation. A multivariate version of such a decomposition is
presented in the paper for a class of random fields generated by several commuting, noninvertible, probability preserving
transformations In this representation, summands of mixed type appear, which behave with respect to some group of directions
of the parameter space as reversed rnultiparameter martingale differences (in the sense of one of several known definitions),
while they look as coboundaries relative to other directions. Applications to limit theorems will be published elsewhere.
Bibliography: 14 titles. 相似文献
8.
Hans-Peter Scheffler 《Probability Theory and Related Fields》2000,116(2):257-271
For a random vector belonging to the (generalized) domain of operator semistable attraction of some nonnormal law we prove
various variants of Chover's law of the iterated logarithm for the partial sum. Furthermore we also derive some large deviation
results necessary for the proof of our main theorems.
Received: 30 September 1998 / Revised version: 28 May 1999 相似文献
9.
In this paper we derive limit theorems of some general functions of independent and identically distributed random variables. A stability property is used to derive the limit theory for general functions. A procedure followed in de Haan (1976) and Leadbetter et al. (1983) is used to prove the main result. The limit theorems for the maximum, minimum and sum of fixed sample sizes and random sample sizes are derived as special cases of the main result. 相似文献
10.
E. A. Chernavskaya 《Moscow University Mathematics Bulletin》2016,71(6):257-260
We consider an infinite-server queueing system where customers come by groups of random size at random i.d. intervals of time. The number of requests in a group and intervals between their arrivals can be dependent. We assume that service times have a regularly varying distribution with infinite mean. We obtain limit theorems for the number of customers in the system and prove limit theorems under appropriate normalizations. 相似文献
11.
Timo Seppäläinen 《Probability Theory and Related Fields》1995,101(4):547-576
Summary We transform nonstationary independent random fields with exponential Radon-Nikodym factors and study the asymptotics of the transformed processes. As applications we deduce conditional limit theorems for such random fields, and we study a Curie-Weiss-type mean-field model of a quenched mixed magnetic crystal. This model has quenched site disorder and frustration but non-random coupling constants. We find a continuous phase transition with critical exponents equal to those of the classical Curie-Weiss theory. 相似文献
12.
Yuri Bakhtin 《Random Structures and Algorithms》2010,37(3):312-331
We consider Gibbs distributions on finite random plane trees with bounded branching. We show that as the order of the tree grows to infinity, the distribution of any finite neighborhood of the root of the tree converges to a limit. We compute the limiting distribution explicitly and study its properties. We introduce an infinite random tree consistent with these limiting distributions and show that it satisfies a certain form of the Markov property. We also study the growth of this tree and prove several limit theorems including a diffusion approximation. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010 相似文献
13.
We prove Berry–Esseen type rates of convergence for central limit theorems (CLTs) of regenerative processes which generalize previous results of Bolthausen under weaker moment assumptions. We then show how this general result can be applied to obtain rates of convergence for (1) CLTs for additive functionals of positive recurrent Markov chains under certain conditions on the strong mixing coefficients, and (2) annealed CLTs for certain ballistic random walks in random environments. 相似文献
14.
A continuous time random walk (CTRW) is a random walk subordinated to a renewal process, used in physics to model anomalous diffusion. Transition densities of CTRW scaling limits solve fractional diffusion equations. This paper develops more general limit theorems, based on triangular arrays, for sequences of CTRW processes. The array elements consist of random vectors that incorporate both the random walk jump variable and the waiting time preceding that jump. The CTRW limit process consists of a vector-valued Lévy process whose time parameter is replaced by the hitting time process of a real-valued nondecreasing Lévy process (subordinator). We provide a formula for the distribution of the CTRW limit process and show that their densities solve abstract space–time diffusion equations. Applications to finance are discussed, and a density formula for the hitting time of any strictly increasing subordinator is developed. 相似文献
15.
M. Kuba 《Discrete Mathematics》2008,308(4):529-540
We introduce random recursive trees, where deterministically weights are attached to the edges according to the labeling of the trees. We will give a bijection between recursive trees and permutations, which relates the arising edge-weights in recursive trees with inversions of the corresponding permutations. Using this bijection we obtain exact and limiting distribution results for the number of permutations of size n, where exactly m elements have j inversions. Furthermore we analyze the distribution of the sum of labels of the elements, which have exactly j inversions, where we can identify Dickman's infinitely divisible distribution as the limit law. Moreover we give a distributional analysis of weighted depths and weighted distances in edge-weighted recursive trees. 相似文献
16.
A branching process counted by a random characteristic has been defined as a process which at time t is the superposition of individual stochastic processes evaluated at the actual ages of the individuals of a branching population. Now characteristics which may depend not only on age but also on absolute time are considered. For supercritical processes a distributional limit theorem is proved, which implies that classical limit theorems for sums of characteristics evaluated at a fixed age point transfer into limit theorems for branching processes counted by these characteristics. A point is that, though characteristics of different individuals should be independent, the characteristics of an individual may well interplay with the reproduction of the latter. The result requires a sort of Lp-continuity for some 1 ? p ? 2. Its proof turns out to be valid for a wider class of processes than branching ones.For the case p = 1 a number of Poisson type limits follow and for p = 2 some normality approximations are concluded. For example results are obtained for processes for rare events, the age of the oldest individual, and the error of population predictions.This work has been supported by a grant from the Swedish Natural Science Research Council. 相似文献
17.
In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems for these non-linear functions when they converge in law to a normal distribution. 相似文献
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Summary Suppose that i.i.d. random variables are attached to the edges of an infinite tree. When the tree is large enough, the partial sumsS
along some of its infinite paths will exhibit behavior atypical for an ordinary random walk. This principle has appeared in works on branching random walks, first-passage percolation, and RWRE on trees. We establish further quantitative versions of this principle, which are applicable in these settings. In particular, different notions of speed for such a tree-indexed walk correspond to different dimension notions for trees. Finally, if the labeling variables take values in a group, then properties of the group (e.g., polynomial growth or a nontrivial Poisson boundary) are reflected in the sample-path behavior of the resulting tree-indexed walk.Partially supported by a grant from the Landau Center for Mathematical AnalysisPartially supported by NSF grant DMS-921 3595 相似文献
20.
Adam Bowditch 《Stochastic Processes and their Applications》2019,129(3):740-770
We prove CLTs for biased randomly trapped random walks in one dimension. By considering a sequence of regeneration times, we will establish an annealed invariance principle under a second moment condition on the trapping times. In the quenched setting, an environment dependent centring is necessary to achieve a central limit theorem. We determine a suitable expression for this centring. As our main motivation, we apply these results to biased walks on subcritical Galton–Watson trees conditioned to survive for a range of bias values. 相似文献