共查询到20条相似文献,搜索用时 31 毫秒
1.
A multiplicative cascade can be thought of as a randomization of a measure on the boundary of a tree, constructed from an iid collection of random variables attached to the tree vertices. Given an initial measure with certain regularity properties, we construct a continuous time, measure-valued process whose value at each time is a cascade of the initial one. We do this by replacing the random variables on the vertices with independent increment processes satisfying certain moment assumptions. Our process has a Markov property: at any given time it is a cascade of the process at any earlier time by random variables that are independent of the past. It has the further advantage of being a martingale and, under certain extra conditions, it is also continuous. For Gaussian independent increment processes we develop the infinite-dimensional stochastic calculus that describes the evolution of the measure process, and use it to compute the optimal Hölder exponent in the Wasserstein distance on measures. We also discuss applications of this process to the model of tree polymers. 相似文献
2.
《Stochastic Processes and their Applications》1986,23(2):269-279
Allowing an offspring probability distribution that has infinite variances, we establish the convergence in finite-dimensional distributions of normalized critical multitype Galton-Watson branching processes with increasing initial population size in the two cases of not conditioning and of conditioning on non-extinction of the processes in the nth generation. Furthermore, if the offspring probability distribution has only finite variances, we show that some linear functions of the above processes weakly converge to the diffusions given by Feller, and by Lamperti and Ney. 相似文献
3.
Shi-xia Ma 《应用数学学报(英文版)》2006,22(3):419-428
In this paper, we consider a bisexual Galton-Watson branching process whose offspring probability distribution is controlled by a random environment proccss. Some results for the probability generating functions associated with the process are obtained and sufficient conditions for certain extinction and for non-certain extinction are established. 相似文献
4.
We define trees generated by bi-infinite sequences, calculate their walk-invariant distribution and the speed of a biased random walk. We compare a simple random walk on a tree generated by a bi-infinite sequence with a simple random walk on an augmented Galton-Watson tree. We find that comparable simple random walks require the augmented Galton-Watson tree to be larger than the corresponding tree generated by a bi-infinite sequence. This is due to an inequality for random variables with values in [1, [ involving harmonic, geometric and arithmetic mean. 相似文献
5.
O. V. Viskov 《Mathematical Notes》1970,8(4):701-705
The determination of the total number of particles taking part in a Galton-Watson process up to its extinction is reduced to the summation of independent, mutually independent random variables. The joint distribution of the total number of particles and the total duration of particles is investigated for branching processes with metamorphoses depending on age.Translated from Matematicheskie Zametki, Vol. 8, No. 4, pp. 409–418, October, 1970. 相似文献
6.
7.
Richard A. Johnson V. Susarla John van Ryzin 《Stochastic Processes and their Applications》1979,9(3):307-318
The purpose of this paper is to obtain Bayes estimators for both the offspring and life-length distribution in the context of a Bellman-Harris age-dependent branching process. We take a non-parametric approach by letting the prior random distributions, for the offspring and life-length distributions, be independent Dirichlet processes. Our primary results concern the derivation of Bayes estimators, under weighted squared error loss for each distribution. We also indicate some of their asymptotic properties and briefly discuss the modifications that become necessary when the initial information is such that the prior random distribution cannot be taken to be independent. 相似文献
8.
Age-dependent branching processes in random environments 总被引:4,自引:0,他引:4
We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ0,ξ1,...) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξn) on R , and reproduce independently new particles according to a probability law p(ξn) on N. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean EξZ(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments. 相似文献
9.
10.
One considers two schemes of the Bellman-Harris process with immigration when a) the lifetime of the particles is an integral-valued random variable and the immigration is defined by a sequence of independent random variables; b) the distribution of the lifetime of the particles is nonlattice and the immigration is a process with continuous time. One investigates the properties of the life spans of such processes. The results obtained here are a generalization to the case of Bellman-Harris processes of the results of A. M. Zubkov, obtained for Markov branching processes. For the proof one makes use in an essential manner of the known inequalities of Goldstein, estimating the generating function of the Bellman-Harris process in terms of the generating functions of the imbedded Galton-Watson process.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 60–82, 1986. 相似文献
11.
In this article, the population-size-dependent bisexual Galton-Watson processes are considered. Under some suitable conditions on the mating functions and the offspring distribution, existence of the limit of mean growth rate per mating unit is proved. And based on the limit, a criterion to identify whether the process admits ultimate extinct with probability one is obtained. 相似文献
12.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(12):1207-1212
We consider a non-negative martingale, defined by sums of product of non-negative random weights indexed by nodes of a Galton-Watson tree. In case the limit variable is not degenerate, we study the asymptotic behaviour at infinity of its distribution; in the contrary case, we prove that there is an associated natural martingale which converges to a non-negative random variable with infinite mean. The two limit variables satisfy the same distributional equation. 相似文献
13.
The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as
infinite total edge length and vertices with infinite branching degree. Aldous's Brownian continuum random tree, the random
tree-like object naturally associated with a standard Brownian excursion, may be thought of as a random compact real tree.
The continuum random tree is a scaling limit as N→∞ of both a critical Galton-Watson tree conditioned to have total population size N as well as a uniform random rooted combinatorial tree with N vertices. The Aldous–Broder algorithm is a Markov chain on the space of rooted combinatorial trees with N vertices that has the uniform tree as its stationary distribution. We construct and study a Markov process on the space of
all rooted compact real trees that has the continuum random tree as its stationary distribution and arises as the scaling
limit as N→∞ of the Aldous–Broder chain. A key technical ingredient in this work is the use of a pointed Gromov–Hausdorff distance to
metrize the space of rooted compact real trees.
Berkeley Statistics Technical Report No. 654 (February 2004), revised October 2004. To appear in Probability Theory and Related Fields.
SNE supported in part by NSF grants DMS-0071468 and DMS-0405778, and a Miller Institute for Basic Research in Science research
professorship
JP supported in part by NSF grants DMS-0071448 and DMS-0405779
AW supported by a DFG Forchungsstipendium 相似文献
14.
Fred M. Hoppe 《Aequationes Mathematicae》1980,20(1):33-37
It is shown that a 1-1 correspondence exists between the possible Yaglom conditional limits when a subcritical Galton-Watson process is initiated with an arbitrary probability distribution and the invariant measures of the process. This is proven by an examination of the relevant Schröder and Abel functional equations. 相似文献
15.
16.
O. V. Rusakov 《Journal of Mathematical Sciences》2009,159(3):350-357
We describe a construction in which the discrete time of a sequence of independent, identically distributed random variables
changes with the Poisson time. The Poisson time is independent of this sequence. The defined process with continuous time
is called a random index process. We establish several properties of random index processes. We study asymptotics of sums
of independent, identically distributed random index processes in the case where elements of the initial sequence have strictly
α-stable distribution. By calculating characteristic functions we establish relationships of these sums with strictly α-stable
processes of the Ornstein- Uhlenbeck type. Bibliography: 4 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 361, 2008, pp. 123–137. 相似文献
17.
S?awomir Dinew 《Mathematische Zeitschrift》2009,262(1):1-15
We generalize an inequality for mixed Monge–Ampère measures from Kołodziej (Indiana Univ. Math. J. 43, 1321–1338, 1994). We also give an example that shows that our assumptions are sharp. The corresponding result in the setting
of compact K?hler manifold is also discussed. 相似文献
18.
A. M. Denisov 《Proceedings of the Steklov Institute of Mathematics》2013,282(1):80-89
We investigate a multitype Galton-Watson process in a random environment generated by a sequence of independent identically distributed random variables. Assuming that the mean of the increment X of the associated random walk constructed by the logarithms of the Perron roots of the reproduction mean matrices is negative and the random variable Xe X has zero mean, we find the asymptotics of the survival probability at time n as n → ∞. 相似文献
19.
A new class of models, which combines closed queueing networks with branching processes, is introduced. The motivation comes
from MIMD computers and other service systems in which the arrival of new work is always triggered by the completion of former
work, and the amount of arriving work is variable. In the variant of branching/queueing networks studied here, a customer
branches into a random and state-independent number of offspring upon completing its service. The process regenerates whenever
the population becomes extinct. Implications for less rudimentary variants are discussed. The ergodicity of the network and
several other aspects are related to the expected total number of progeny of an associated multitype Galton-Watson process.
We give a formula for that expected number of progeny. The objects of main interest are the stationary state distribution
and the throughputs. Closed-form solutions are available for the multi-server single-node model, and for homogeneous networks
of infinite-servers. Generally, branching/queueing networks do not seem to have a product-form state distribution. We propose
a conditional product-form approximation, and show that it is approached as a limit by branching/queueing networks with a
slowly varying population size. The proof demonstrates an application of the nearly complete decomposability paradigm to an
infinite state space.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
This note develops theory and a solution technique for a quadratically constrained eigenvalue minimization problem. This class
of problems arises in the numerical solution of fully-nonlinear boundary value problems of Monge–Ampère type. Though it is
most important in the three dimensional case, the solution method is directly applicable to systems of arbitrary dimension.
The focus here is on solving the minimization subproblem which is part of a method to numerically solve a Monge–Ampère type
equation. These subproblems must be evaluated many times in this numerical solution technique and thus efficiency is of utmost
importance. A novelty of this minimization algorithm is that it is finite, of complexity O(n3)\mathcal{O}(n^3), with the exception of solving a very simple rational function of one variable. This function is essentially the same for
any dimension. This result is quite surprising given the nature of the constrained minimization problem. 相似文献