共查询到20条相似文献,搜索用时 956 毫秒
1.
Pei-Sen Li 《Stochastic Processes and their Applications》2019,129(8):2941-2967
A continuous-state polynomial branching process is constructed as the pathwise unique solution of a stochastic integral equation with absorbing boundary condition. The process can also be obtained from a spectrally positive Lévy process through Lamperti type transformations. The extinction and explosion probabilities and the mean extinction and explosion times are computed explicitly. Some of those are also new for the classical linear branching process. We present necessary and sufficient conditions for the process to extinguish or explode in finite times. In the critical or subcritical case, we give a construction of the process coming down from infinity. Finally, it is shown that the continuous-state polynomial branching process arises naturally as the rescaled limit of a sequence of discrete-state processes. 相似文献
2.
Peter Braunsteins Geoffrey Decrouez Sophie Hautphenne 《Stochastic Processes and their Applications》2019,129(3):713-739
We consider the extinction events of Galton–Watson processes with countably infinitely many types. In particular, we construct truncated and augmented Galton–Watson processes with finite but increasing sets of types. A pathwise approach is then used to show that, under some sufficient conditions, the corresponding sequence of extinction probability vectors converges to the global extinction probability vector of the Galton–Watson process with countably infinitely many types. Besides giving rise to a family of new iterative methods for computing the global extinction probability vector, our approach paves the way to new global extinction criteria for branching processes with countably infinitely many types. 相似文献
3.
本文在文献[6]的基础上,集中考虑一类带灾难的非线性马尔可夫分枝过程的基本问题-唯一性,正则性和灭绝性。文章首先给出其Q-过程唯一性的证明,然后得出该畔程的正则性与[3]非线性马尔币夫分枝过程一样,最后,我们给出该Q-过程以概1l灭绝的充要条件是Q-过程正则。 相似文献
4.
We consider a very general interacting branching process which includes most of the important interacting branching models considered so far. After obtaining some key preliminary results, we first obtain some elegant conditions regarding regularity and uniqueness. Then the extinction vector is obtained which is very easy to be calculated. The mean extinction time and the conditional mean extinction time are revealed. The mean explosion time and the total mean life time of the processes are also investigated and resolved. 相似文献
5.
Anyue Chen 《Journal of Mathematical Analysis and Applications》2002,274(2):482-494
This paper focuses on the basic problems regarding uniqueness and extinction properties for generalised Markov branching processes. The uniqueness criterion is firstly established and a differential-integral equation satisfied by the transition functions of such processes is derived. The extinction probability is then obtained. A closed form is presented for both the mean extinction time and the conditional mean extinction time. It turns out that these important quantities are closely related to the elementary gamma function. 相似文献
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We study infinite horizon control of continuous-time non-linear branching processes with almost sure extinction for general (positive or negative) discount. Our main goal is to study the link between infinite horizon control of these processes and an optimization problem involving their quasi-stationary distributions and the corresponding extinction rates. More precisely, we obtain an equivalent of the value function when the discount parameter is close to the threshold where the value function becomes infinite, and we characterize the optimal Markov control in this limit. To achieve this, we present a new proof of the dynamic programming principle based upon a pseudo-Markov property for controlled jump processes. We also prove the convergence to a unique quasi-stationary distribution of non-linear branching processes controlled by a Markov control conditioned on non-extinction. 相似文献
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Galton-Watson分支过程的谱半径的概率刻画 总被引:1,自引:1,他引:0
谱半径是不可约马尔可夫链的一个很重要的特征数字.Galton-Watson分支过程是一类特殊的马尔可夫链,我们已经证明了在不可约的条件下,Galton-Watson分支过程的谱半径等于其对应的概率母函数f(s)在灭绝概率q点的导数值.本文主要从理论上刻画从过程的任何状态逃离速度的Galton-Watson分支过程的谱半径的概率意义. 相似文献
10.
A new class of branching models, the general collision branching processes with two parameters, is considered in this paper.
For such models, it is necessary to evaluate the absorbing probabilities and mean extinction times for both absorbing states.
Regularity and uniqueness criteria are firstly established. Explicit expressions are then obtained for the extinction probability
vector, the mean extinction times and the conditional mean extinction times. The explosion behavior of these models is investigated
and an explicit expression for mean explosion time is established. The mean global holding time is also obtained. It is revealed
that these properties are substantially different between the super-explosive and sub-explosive cases.
This work was partially supported by National Natural Science Foundation of China (Grant No. 10771216), Research Grants Council
of Hong Kong (Grant No. HKU 7010/06P) and Scientific Research Foundation for Returned Overseas Chinese Scholars, State Education
Ministry of China (Grant No. [2007]1108) 相似文献
11.
David Tanny 《Stochastic Processes and their Applications》1978,6(2):201-211
Normalizing constants are obtained for B.P.R.E. such that the limiting random variable is finite almost everywhere and is zero only on the extinction set of the process w.p.1. Furthermore, the normalizing constants can be chosen so that they grow exponentially fast, and so that the ratio of successive constants converges in distribution. The method of proof used is to prove the result for increasing branching processes, and then, to transfer the result to general B.P.R.E. by employing the relationships between B.P.R.E., the associated B.P.R.E., and the reduced branching process. 相似文献
12.
Anyue Chen Phil Pollett Junping Li Hanjun Zhang 《Methodology and Computing in Applied Probability》2010,12(3):511-531
We examine basic properties regarding uniqueness, extinction, and explosivity for the generalised Markov branching processes
with pairwise interaction. First we establish uniqueness criteria, proving that in the essentially-explosive case the process
is honest if and only if the mean death rate is greater than or equal to the mean birth rate, while in the sub-explosive case
the process is dishonest only in exceptional circumstances. Explicit expressions are then obtained for the extinction probabilities,
the mean extinction times and the conditional mean extinction times. Explosivity is also investigated and an explicit expression
for mean explosion time is established. 相似文献
13.
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
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Yuhui ZHANG 《Frontiers of Mathematics in China》2018,13(5):1215-1243
Based on an explicit representation of moments of hitting times for single death processes, the criteria on ergodicity and strong ergodicity are obtained. These results can be applied for an extended class of branching processes. Meanwhile, some sufficient and necessary conditions for recurrence and exponential ergodicity as well as extinction probability for the processes are presented. 相似文献
17.
S. Ma M. Molina Y. Xing 《Stochastics An International Journal of Probability and Stochastic Processes》2016,88(1):147-161
We model the demographic dynamics of populations with sexual reproduction where the reproduction phase occurs in a non-predictable environment and we assume the immigration/out-migration of mating units in the population. We introduce a general class of two-sex branching processes where, in each generation, the number of mating units which take part in the reproduction phase is randomly determined and the offspring probability distribution changes over time in a random environment. We provide several probabilistic results about the limit behaviour of populations whose dynamics is modelled by such a class of stochastic processes. In particular, we provide sufficient conditions for the almost sure extinction of the population or for its survival with a positive probability. As illustration, we include some simulated examples. 相似文献
18.
Abstract Some classes of controlled branching processes (with nonhomo-geneous migration or with nonhomo-geneous state-dependent immigration) lead in the critical case to a recurrence for the extinction probabilities. Under some additional conditions it is known that this recurrence depends on some parameter β and converges for 0 < β < 1. Now we show that the recurrence does converge for all positive values of the parameter β, which leads to an extension of some limit theorems for the corresponding branching processes. We also give a generalization of the recurrence and an asymptotic analysis of its behavior. 相似文献
19.
Yan Xia REN 《数学学报(英文版)》2008,24(2):275-284
The global supports of super-Poisson processes and super-random walks with a branching mechanism ψ(z)=z^2 and constant branching rate are known to be noncompact. It turns out that, for any spatially dependent branching rate, this property remains true. However, the asymptotic extinction property for these two kinds of superprocesses depends on the decay rate of the branching-rate function at infinity. 相似文献
20.
Sophie Hautphenne Guy Latouche Marie-Ange Remiche 《Methodology and Computing in Applied Probability》2011,13(1):171-192
The extinction probability of a branching process is characterized as the solution of a fixed-point equation which, for a
fairly general class of Markovian branching processes, is vector quadratic. We address the question of solving that equation,
using a mixture of algorithmic and probabilistic arguments. We compare the relative efficiency of three iterative methods
based on functional iteration, on the basis of the probabilistic interpretation of the successive iterations as well as on
the basis of traditional rate of convergence analysis. We illustrate our findings through a few numerical examples and conclude
by showing how they extend to more complex systems. 相似文献