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

1974 ◽  
Vol 11 (4) ◽  
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.

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.

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 properties of super-critical branching processes II: Crump-Mode and Jirina processes

1975 ◽  
Vol 7 (01) ◽  
pp. 66-82 ◽  
Author(s):  
N. H. Bingham ◽  
R. A. Doney
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Regular Variation ◽  
Branching Processes ◽  
Asymptotic Properties ◽  
Random Variables ◽  
The Other ◽  
Continuous State Space ◽  
Continuous State ◽  
Integer Exponent

We obtain results connecting the distribution of the random variablesYandWin the supercritical generalized branching processes introduced by Crump and Mode. For example, if β > 1,EYβandEWβconverge or diverge together and regular variation of the tail of one ofY, Wwith non-integer exponent β > 1 is equivalent to regular variation of the other. We also prove analogous results for the continuous-time continuous state-space branching processes introduced by Jirina.

Asymptotic properties of super-critical branching processes II: Crump-Mode and Jirina processes

1975 ◽  
Vol 7 (1) ◽  
pp. 66-82 ◽  
Author(s):  
N. H. Bingham ◽  
R. A. Doney
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Regular Variation ◽  
Branching Processes ◽  
Asymptotic Properties ◽  
Random Variables ◽  
The Other ◽  
Continuous State Space ◽  
Continuous State ◽  
Integer Exponent

We obtain results connecting the distribution of the random variables Y and W in the supercritical generalized branching processes introduced by Crump and Mode. For example, if β > 1, EYβ and EWβ converge or diverge together and regular variation of the tail of one of Y, W with non-integer exponent β > 1 is equivalent to regular variation of the other. We also prove analogous results for the continuous-time continuous state-space branching processes introduced by Jirina.

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

2006 ◽  
Vol 43 (1) ◽  
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.

Randomization of intensities in a Markov chain

1979 ◽  
Vol 11 (2) ◽  
pp. 397-421 ◽  
Author(s):  
M. Yadin ◽  
R. Syski
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
State Space ◽  
Continuous Time ◽  
Markovian Process ◽  
Time Parameter ◽  
Discrete State ◽  
Intensity Matrix ◽  
The Matrix ◽  
Discrete State Space

The matrix of intensities of a Markov process with discrete state space and continuous time parameter undergoes random changes in time in such a way that it stays constant between random instants. The resulting non-Markovian process is analyzed with the help of supplementary process defined in terms of variations of the intensity matrix. Several examples are presented.

A STATISTICAL METHOD FOR DETECTING CYCLES IN DISCRETE DYNAMICAL SYSTEMS

1996 ◽  
Vol 06 (12a) ◽  
pp. 2375-2388 ◽  
Author(s):  
MARKUS LOHMANN ◽  
JAN WENZELBURGER
Keyword(s):  
Dynamical Systems ◽  
State Space ◽  
Statistical Method ◽  
Basins Of Attraction ◽  
Discrete State ◽  
Continuous State Space ◽  
Continuous State ◽  
Long Term Behavior ◽  
Discrete Time Dynamical Systems

This paper introduces a statistical method for detecting cycles in discrete time dynamical systems. The continuous state space is replaced by a discrete one consisting of cells. Hashing is used to represent the cells in the computer’s memory. An algorithm for a two-parameter bifurcation analysis is presented which uses the statistical method to detect cycles in the discrete state space. The output of this analysis is a colored cartogram where parameter regions are marked according to the long-term behavior of the system. Moreover, the algorithm allows the computation of basins of attraction of cycles.

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