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1.
This paper focuses on discussing some basic properties of the weighted Markov branching process which is a natural generalisation
of the ordinary Markov branching process. The regularity and uniqueness criteria, which are very easy to verify, are firstly
established. Some important characteristics regarding the hitting times of such structure are obtained. In particular, the
closed forms for the mean extinction time and conditional mean extinction time are presented. The explosion behaviour of the
process is investigated and then the mean explosion time is derived. The mean global holding time and the mean total survival
time are also obtained.
AMS 2000 Subject Classification Primary 60 J27; Secondary 60 J80 相似文献
2.
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
3.
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
4.
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
5.
JunPing Li 《中国科学A辑(英文版)》2009,52(5):875-894
We consider the decay parameter, invariant measures/vectors and quasi-stationary dis- tributions for 2-type Markov branching processes. Investigating such properties is crucial in realizing life period of branching models. In this paper, some important properties of the generating functions for 2-type Markov branching q-matrix are firstly investigated in detail. The exact value of the decay parameter λC of such model is given for the communicating class C = Z+2 \ 0. It is shown that this λC can be directly ... 相似文献
6.
7.
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
8.
We propose a minimum mean absolute error linear interpolator (MMAELI), based on theL
1 approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation
for the coefficients of this linear functional is established in terms of the innovation series. It is found that information
implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations
following mixed normal andt distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI)
well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented.
Extensions to the general ARMA model and other time series models are discussed.
This research was supported by a CityU Research Grant and Natural Science Foundation of China. 相似文献
9.
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
10.
Xiangqun Yang 《中国科学A辑(英文版)》1999,42(5):471-477
Of repeated hits and repeated explosions after first explosion for a birth and death process with explosion some properties
are investigated. The properties of repeated hits after first explosion may be expressed by the properties of the first hit
after the first explosion.
Project supported by the National Natural Science Foundation of China (Grant No. 19761028) and the Centre of Researching Mathematics
and Forstering Higher Talent, the Ministry of Education of China. 相似文献
11.
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
12.
LI JunPing & LIU ZaiMing School of Mathematical Science Computing Technology Central South University Changsha China 《中国科学 数学(英文版)》2011,(5)
We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in detail. The explicit expressions for the extinction probabilities and mean extinction times are presented. The ergodicity and stability properties of the process incorporating with resurrection structure are then investigated. The conditions for recurrence, ergodicity and exponential ergodicity are... 相似文献
13.
We use a new approach to consider the extinction properties of the Markov branching process with immigration and migration recently discussed by Li and Liu [Sci. China Math., 2011, 54: 1043–1062]. Some much better explicit expressions are obtained for the extinction probabilities of the subtle super-interacting case. 相似文献
14.
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
15.
Criterion on the limits of superprocesses 总被引:1,自引:0,他引:1
Yongjin Wang 《中国科学A辑(英文版)》1998,41(8):849-858
Starting with super-diffusion processes, the asymptotic behavior of the superprocesses on finite and infinite measure spaces
is systematically studied by general branching mechanisms. The complete features of their limits are described and a criterion
on their behavior is presented.
Project supported by the National Natural Science Foundation of China (Grant No. 19631010) and the Mathematical Centre of
the State Education Commission. 相似文献
16.
Convergence of Newton‘’s Method and Uniqueness of the Solution of Equations in Banach SpacesⅡ 总被引:7,自引:0,他引:7
XingHuaWANG ChongLI 《数学学报(英文版)》2003,19(2):405-412
Some results on convergence of Newton‘s method in Banach spaces are established under the assumption that the derivative of the opderators satisfies the radius or center Lipschitz condition with a weak L average. 相似文献
17.
AR and bilinear time series models are expressed as time series chain graphical models, based on which, it is shown that the
coefficients of AR and bilinear models are the conditional correlation coefficients conditioned on the other components of
the time series. Then a graphically based procedure is proposed to test the significance of the coefficients of AR and bilinear
time series. Simulations show that our procedure performs well both in sizes and powers.
This work was supported by the Hong Kong Polytechnic University Research Council, the National Natural Science Foundation
of China (Grant No. 10671044) and the Science and Technology Bureau of Guangzhou Municipal Government of China (Grant No.
LSBH-017) 相似文献
18.
A non-critical branching immigration superprocess with dependent spatial motion is constructed and characterized as the solution of a stochastic equation driven by a time-space white noise and an orthogonal martingale measure. A representation of its conditional log-Laplace functionals is established, which gives the uniqueness of the solution and hence its Markov property. Some properties of the superprocess including an ergodic theorem are also obtained.Mathematics Subject Classifications (2000) 60J80, 60G57, 60J35.Zenghu Li: Supported by the NSFC (No. 10121101 and No. 10131040).Hao Wang: Supported by the research grant of UO.Jie Xiong: Research supported partially by NSA and by Alexander von Humboldt Foundation. 相似文献
19.
This paper deals with the convergence of the Cesaro mean for the rational orthonormal bases. Provided the set of zeroes of rational orthonormal bases is formed by a periodic repetition of the same finite sequence, the explicit expression of so-called block-Fejer kernel is available, and some properties of the block-Fejer kernel are discussed. Based on the convergence of the block-Cesaro mean, the convergence of Cesaro mean is also provided. 相似文献
20.
The Paley-Wiener theorem in the non-commutative and non-associative octonion analytic function space is proved.
This work was supported by the National Basic Research Program of China (Grant No. 1999075105), the National Natural Science
Foundation of China (Grant No. 10471002) and Research Foundation for Doctoral Programm (Grant No. 20050574002) 相似文献