Critical Measure-Valued Branching Processes in Discrete Time with Arbitrary Phase Space, I

1981 ◽  
Vol 103 (1) ◽  
pp. 63-107 ◽  
Author(s):  
K. Hermann
Keyword(s):  
Phase Space ◽  
Discrete Time ◽  
Branching Processes ◽  
Critical Measure ◽  
Arbitrary Phase

scholarly journals Two-Sex Branching Processes with Offspring and Mating in a Random Environment

2009 ◽  
Vol 46 (04) ◽  
pp. 993-1004
Author(s):  
S. Ma ◽  
M. Molina
Keyword(s):  
Mathematical Model ◽  
Probability Distribution ◽  
Discrete Time ◽  
Random Environment ◽  
Generating Functions ◽  
Branching Processes ◽  
Random Vectors ◽  
Environmental Process ◽  
Mating Function ◽  
The Mathematical Model

We introduce a class of discrete-time two-sex branching processes where the offspring probability distribution and the mating function are governed by an environmental process. It is assumed that the environmental process is formed by independent but not necessarily identically distributed random vectors. For such a class, we determine some relationships among the probability generating functions involved in the mathematical model and derive expressions for the main moments. Also, by considering different probabilistic approaches we establish several results concerning the extinction probability. A simulated example is presented as an illustration.

scholarly journals A Limit Theorem for Discrete Galton-Watson Branching Processes with Immigration

2006 ◽  
Vol 43 (01) ◽  
pp. 289-295 ◽  
Author(s):  
Zenghu Li
Keyword(s):  
Limit Theorem ◽  
Weak Convergence ◽  
Discrete Time ◽  
Continuous Time ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Discrete State ◽  
Simple Set ◽  
Continuous State

We provide a simple set of sufficient conditions for the weak convergence of discrete-time, discrete-state Galton-Watson branching processes with immigration to continuous-time, continuous-state branching processes with immigration.

Asymptotic behavior of near-critical multitype branching processes

1991 ◽  
Vol 28 (03) ◽  
pp. 512-519 ◽  
Author(s):  
Fima C. Klebaner
Keyword(s):  
Asymptotic Behavior ◽  
Population Size ◽  
Discrete Time ◽  
Growth Rates ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Limiting Distribution ◽  
Size Dependent ◽  
Generalized Gamma ◽  
Multitype Branching Processes

Sufficient conditions for survival and extinction of multitype population-size-dependent branching processes in discrete time are obtained. Growth rates are determined on the set of divergence to infinity. The limiting distribution of a properly normalized process can be generalized gamma, normal or degenerate.

A branching-process solution of the polydisperse coagulation equation

1984 ◽  
Vol 16 (01) ◽  
pp. 56-69 ◽  
Author(s):  
John L. Spouge
Keyword(s):  
Discrete Time ◽  
Branching Process ◽  
Branching Processes ◽  
Critical Time ◽  
Coagulation Equation ◽  
Multitype Branching Processes ◽  
Irreversible Aggregation ◽  
Image Position ◽  
Supercritical Branching Processes ◽  
Critical Branching Process

The polydisperse coagulation equation models irreversible aggregation of particles with varying masses. This paper uses a one-parameter family of discrete-time continuous multitype branching processes to solve the polydisperse coagulation equation when The critical time tc when diverges corresponds to a critical branching process, while post-critical times t> tc correspond to supercritical branching processes.

Asymptotic behaviour of continuous time, continuous state-space branching processes

1974 ◽  
Vol 11 (04) ◽  
pp. 669-677 ◽  
Author(s):  
D. R. Grey
Keyword(s):  
Asymptotic Behaviour ◽  
State Space ◽  
Discrete Time ◽  
Continuous Time ◽  
Branching Processes ◽  
Discrete State ◽  
Space And Time ◽  
Continuous State Space ◽  
Continuous State ◽  
Discrete State Space

Results on the behaviour of Markov branching processes as time goes to infinity, hitherto obtained for models which assume a discrete state-space or discrete time or both, are here generalised to a model with both state-space and time continuous. The results are similar but the methods not always so.

Sign in / Sign up

Export Citation Format

Share Document