scholarly journals Controlled branching processes with continuous time

2021 ◽  
Vol 58 (3) ◽  
pp. 830-848
Author(s):  
Miguel González ◽  
Manuel Molina ◽  
Ines del Puerto ◽  
Nikolay M. Yanev ◽  
George P. Yanev
Keyword(s):  
Continuous Time ◽  
Critical Case ◽  
Branching Processes ◽  
Asymptotic Properties ◽  
Limiting Distributions ◽  
Controlled Branching Processes

AbstractA class of controlled branching processes with continuous time is introduced and some limiting distributions are obtained in the critical case. An extension of this class as regenerative controlled branching processes with continuous time is proposed and some asymptotic properties are considered.

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.

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.

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.

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.

scholarly journals Asymptotic behaviour of critical controlled branching processes with random control functions

2005 ◽  
Vol 42 (2) ◽  
pp. 463-477 ◽  
Author(s):  
M. González ◽  
M. Molina ◽  
I. del Puerto
Keyword(s):  
Asymptotic Behaviour ◽  
Critical Case ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Control Functions ◽  
Limiting Behaviour ◽  
Controlled Branching Processes ◽  
Random Control

In this paper, we investigate the asymptotic behaviour of controlled branching processes with random control functions. In a critical case, we establish sufficient conditions for both their almost-sure extinction and for their nonextinction with a positive probability. For some suitably chosen norming constants, we also determine different kinds of limiting behaviour for this class of processes.

scholarly journals Asymptotic behaviour of critical controlled branching processes with random control functions

2005 ◽  
Vol 42 (02) ◽  
pp. 463-477 ◽  
Author(s):  
M. González ◽  
M. Molina ◽  
I. del Puerto
Keyword(s):  
Asymptotic Behaviour ◽  
Critical Case ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Control Functions ◽  
Limiting Behaviour ◽  
Controlled Branching Processes ◽  
Random Control

In this paper, we investigate the asymptotic behaviour of controlled branching processes with random control functions. In a critical case, we establish sufficient conditions for both their almost-sure extinction and for their nonextinction with a positive probability. For some suitably chosen norming constants, we also determine different kinds of limiting behaviour for this class of processes.

scholarly journals On Estimation of the Convergence Rate to Invariant Measures in Markov Branching Processes with Possibly Infinite Variance and Allowing Immigration

2021 ◽  
Vol 14 (5) ◽  
pp. 573-583
Author(s):  
Azam A. Imomov ◽  
Keyword(s):  
Generating Functions ◽  
Continuous Time ◽  
Branching Process ◽  
Critical Case ◽  
Invariant Measures ◽  
Branching Processes ◽  
Immigration Law ◽  
Infinite Variance ◽  
Transition Functions ◽  
First Moment

The paper discusses the continuous-time Markov Branching Process allowing Immigration. We are considering a critical case for which the second moment of offspring law and the first moment of immigration law are possibly infinite. Assuming that the nonlinear parts of the appropriate generating functions are regularly varying in the sense of Karamata, we prove theorems on convergence of transition functions of the process to invariant measures. We deduce the speed rate of these convergence providing that slowly varying factors are with remainder

Asymptotic properties of the stationary measure of a Markov branching process

1973 ◽  
Vol 10 (02) ◽  
pp. 447-450 ◽  
Author(s):  
Y. S. Yang
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Branching Process ◽  
Critical Case ◽  
Asymptotic Properties ◽  
Stationary Measure ◽  
Infinite Variance ◽  
Finite Variance ◽  
Renewal Theorem ◽  
Markov Branching Process

The asymptotic properties of the unique stationary measure of a Markov branching process will be given. In the critical case with finite variance, the result can be deduced from a result for discrete time processes of Kesten, Ney and Spitzer (1966) where the proof makes use of a stronger assumption than the finiteness of variance. For the continuous time case where the stationary measure has an explicit form, we can use the discrete renewal theorem which takes care of the infinite variance case as well.

Asymptotic properties of the stationary measure of a Markov branching process

1973 ◽  
Vol 10 (2) ◽  
pp. 447-450 ◽  
Author(s):  
Y. S. Yang
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Branching Process ◽  
Critical Case ◽  
Asymptotic Properties ◽  
Stationary Measure ◽  
Infinite Variance ◽  
Finite Variance ◽  
Renewal Theorem ◽  
Markov Branching Process

The asymptotic properties of the unique stationary measure of a Markov branching process will be given. In the critical case with finite variance, the result can be deduced from a result for discrete time processes of Kesten, Ney and Spitzer (1966) where the proof makes use of a stronger assumption than the finiteness of variance. For the continuous time case where the stationary measure has an explicit form, we can use the discrete renewal theorem which takes care of the infinite variance case as well.

Continuous-time Controlled Branching Processes

2021 ◽  
Author(s):  
Inés M.del Puerto ◽  
George P. Yanev ◽  
Manuel Molina ◽  
Nikolay M. Yanev ◽  
Miguel González
Keyword(s):  
Continuous Time ◽  
Branching Processes ◽  
Controlled Branching Processes
Sign in / Sign up

Export Citation Format

Share Document