Branching Processes with Two Types Emigration and State-Dependent Immigration

1996 ◽  
pp. 216-228 ◽  
Author(s):  
George P. Yanev ◽  
Nickolay M. Yanev
Keyword(s):  
Branching Processes ◽  
State Dependent

On two classes of interacting stochastic processes arising in cancer modeling

1983 ◽  
Vol 15 (4) ◽  
pp. 695-712 ◽  
Author(s):  
Robert Bartoszyński ◽  
Prem S. Puri
Keyword(s):  
Markov Processes ◽  
Branching Processes ◽  
The Other ◽  
Time Interval ◽  
Positive Probability ◽  
Martingale Convergence Theorem ◽  
Limiting Behavior ◽  
State Dependent ◽  
Cancer Modeling ◽  
Martingale Convergence

The processes X and Y are said to interact if the laws governing the changes of either of them at time t depend on the values of the other process at times up to t. For bivariate interacting Markov processes, their limiting behavior is analysed by means of an approximation suggested by Fuhrmann, consisting of discretizing time, and assuming that in each time interval the processes develop independently, according to the laws obtained by fixing the value of the other process at its level attained at the beginning of the interval.In this way the conditions for almost sure extinction, escape to ∞ with positive probability, etc., are obtained (by using the martingale convergence theorem) for state-dependent branching processes studied by Roi, and for bivariate processes with one component piecewise determined.

Bellman–Harris branching processes with state-dependent immigration

1985 ◽  
Vol 22 (4) ◽  
pp. 757-765 ◽  
Author(s):  
K. V. Mitov ◽  
N. M. Yanev
Keyword(s):  
Limit Theorem ◽  
Asymptotic Behaviour ◽  
Branching Processes ◽  
The State ◽  
State Dependent ◽  
Probability Of Extinction

We consider critical Bellman-Harris processes which admit an immigration component only in the state 0. The asymptotic behaviour of the probability of extinction and of the first two moments is investigated and a limit theorem is also proved.

Continuous-time branching processes with decreasing state-dependent immigration

1984 ◽  
Vol 16 (4) ◽  
pp. 697-714 ◽  
Author(s):  
K. V. Mitov ◽  
V. A. Vatutin ◽  
N. M. Yanev
Keyword(s):  
Asymptotic Behaviour ◽  
Population Size ◽  
Continuous Time ◽  
Limit Theorems ◽  
Critical Case ◽  
Branching Processes ◽  
State Dependent ◽  
Different Types ◽  
Continuous Time Branching Processes

This paper deals with continuous-time branching processes which allow a temporally-decreasing immigration whenever the population size is 0. In the critical case the asymptotic behaviour of the probability of non-extinction and of the first two moments is investigated and different types of limit theorems are also proved.

Bellman-Harris branching processes with a special type of state-dependent immigration

1989 ◽  
Vol 21 (02) ◽  
pp. 270-283 ◽  
Author(s):  
K. V. Mitov ◽  
N. M. Yanev
Keyword(s):  
Asymptotic Behaviour ◽  
Population Size ◽  
Limit Theorems ◽  
Branching Processes ◽  
State Dependent ◽  
Probability Of Extinction ◽  
New Particles

We investigate critical Bellman-Harris processes which allow immigration of new particles whenever the population size is 0. Under some special conditions on the immigration component the asymptotic behaviour of the probability of extinction is obtained and limit theorems are also proved.

Continuous-time branching processes with decreasing state-dependent immigration

1984 ◽  
Vol 16 (04) ◽  
pp. 697-714 ◽  
Author(s):  
K. V. Mitov ◽  
V. A. Vatutin ◽  
N. M. Yanev
Keyword(s):  
Asymptotic Behaviour ◽  
Population Size ◽  
Continuous Time ◽  
Limit Theorems ◽  
Critical Case ◽  
Branching Processes ◽  
State Dependent ◽  
Different Types ◽  
Continuous Time Branching Processes

This paper deals with continuous-time branching processes which allow a temporally-decreasing immigration whenever the population size is 0. In the critical case the asymptotic behaviour of the probability of non-extinction and of the first two moments is investigated and different types of limit theorems are also proved.

On supercritical Galton-Watson processes allowing immigration

1974 ◽  
Vol 11 (04) ◽  
pp. 814-817 ◽  
Author(s):  
A. G. Pakes
Keyword(s):  
Absolute Continuity ◽  
Branching Processes ◽  
Random Variables ◽  
The Other ◽  
State Dependent ◽  
The Absolute

We establish the absolute continuity of the limit random variables of two supercritical Galton-Watson branching processes, one allowing unrestricted immigration and the other having a state dependent immigration component.

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