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 assoc...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.展开更多
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 gro...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.展开更多
In this article the supercritical bisexual Galton-Watson branching processes with the immigration of mating units is considered. A necessary condition for the almost sure convergence, and a sufficient condition for th...In this article the supercritical bisexual Galton-Watson branching processes with the immigration of mating units is considered. A necessary condition for the almost sure convergence, and a sufficient condition for the L^1 convergence are given for the process with the suitably normed condition.展开更多
This paper discusses a characterization of the members of a subfamily of power series distributions when their probability generating functions satisfy the functional equation where a, b and c are constants and is the...This paper discusses a characterization of the members of a subfamily of power series distributions when their probability generating functions satisfy the functional equation where a, b and c are constants and is the derivative of f.展开更多
The spectral radiuses of Galton-Watson branching processes which describes the speed of the process escaping from any state are calculated. Under the condition of irreducibility,it is show that this is equal to the sp...The spectral radiuses of Galton-Watson branching processes which describes the speed of the process escaping from any state are calculated. Under the condition of irreducibility,it is show that this is equal to the spectral radius of Jacobi matrix of its generating function.展开更多
We construct two kinds of stochastic flows of discrete Galton-Watson branching processes. Some scaling limit theorems for the flows are proved, which lead to local and nonlocal branching superprocesses over the positi...We construct two kinds of stochastic flows of discrete Galton-Watson branching processes. Some scaling limit theorems for the flows are proved, which lead to local and nonlocal branching superprocesses over the positive half line.展开更多
Given a system {S1,…, SN} of N contractive similarities satisfying some strong separation condition, it has an invariant Set K for the system. In this article, the authors construct some random measure μω supported...Given a system {S1,…, SN} of N contractive similarities satisfying some strong separation condition, it has an invariant Set K for the system. In this article, the authors construct some random measure μω supported on random subset Kω of K, μω having some ＂non-standard＂ multifractal structure, which contrasts the well-knoWn multifractal formalism for the invariant measure of system {S1,.., SN} may possess. The main tool is the multifractal structures of a Galton-Watson tree, which are obtained by Liu [9], Shieh-Taylor [14], and MSrters-Shieh [12].展开更多
We first recall some basic facts from the theory of discrete-time Markov chains arising from two types neutral and non-neutral evolution models of population genetics with constant size. We then define and analyze a v...We first recall some basic facts from the theory of discrete-time Markov chains arising from two types neutral and non-neutral evolution models of population genetics with constant size. We then define and analyze a version of such models whose fluctuating total population size is conserved on average only. In our model, the population of interest is seen as being embedded in a frame process which is a critical Galton Watson process. In this context, we address problems such as extinction, fixation, size of the population at fixation and survival probability to a bottleneck effect of the environment.展开更多
文摘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.
文摘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.
基金Supported by the National Natural Science Foundation of China (10871200)
文摘In this article, we obtain the central limit theorem and the law of the iterated logarithm for Galton-Watson processes in i.i.d, random environments.
文摘In this article the supercritical bisexual Galton-Watson branching processes with the immigration of mating units is considered. A necessary condition for the almost sure convergence, and a sufficient condition for the L^1 convergence are given for the process with the suitably normed condition.
文摘This paper discusses a characterization of the members of a subfamily of power series distributions when their probability generating functions satisfy the functional equation where a, b and c are constants and is the derivative of f.
文摘The spectral radiuses of Galton-Watson branching processes which describes the speed of the process escaping from any state are calculated. Under the condition of irreducibility,it is show that this is equal to the spectral radius of Jacobi matrix of its generating function.
基金Acknowledgements The authors would like to give their sincere thanks to Professor Zenghu Li for encouragement and helpful discussion. They also would like to acknowledge the Laboratory of Mathematics and Complex Systems （Ministry of Education, China） for providing them the research facilities. This work was supported in part by the National Natural Science Foundation of China （Grants Nos. 11201030, 11071021, 11126037）, the Specialized Research Fund for the Doctoral Program of Higher Education （20110003120003）, and Ministry of Education （985 Project）.
文摘We construct two kinds of stochastic flows of discrete Galton-Watson branching processes. Some scaling limit theorems for the flows are proved, which lead to local and nonlocal branching superprocesses over the positive half line.
基金Both authors are supported by a grant NSC 2002/3-2115-M-002-017.
文摘Given a system {S1,…, SN} of N contractive similarities satisfying some strong separation condition, it has an invariant Set K for the system. In this article, the authors construct some random measure μω supported on random subset Kω of K, μω having some ＂non-standard＂ multifractal structure, which contrasts the well-knoWn multifractal formalism for the invariant measure of system {S1,.., SN} may possess. The main tool is the multifractal structures of a Galton-Watson tree, which are obtained by Liu [9], Shieh-Taylor [14], and MSrters-Shieh [12].
文摘We first recall some basic facts from the theory of discrete-time Markov chains arising from two types neutral and non-neutral evolution models of population genetics with constant size. We then define and analyze a version of such models whose fluctuating total population size is conserved on average only. In our model, the population of interest is seen as being embedded in a frame process which is a critical Galton Watson process. In this context, we address problems such as extinction, fixation, size of the population at fixation and survival probability to a bottleneck effect of the environment.
