On Conditions of Extinction for the State-Dependent Branching Processes in a Random Environment

2009 ◽  
Vol 53 (4) ◽  
pp. 711-716
Author(s):  
T. K. Fakhrutdinova
Keyword(s):  
Random Environment ◽  
Branching Processes ◽  
The State ◽  
State Dependent

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.

scholarly journals Cell contamination and branching processes in a random environment with immigration

2009 ◽  
Vol 41 (4) ◽  
pp. 1059-1081 ◽  
Author(s):  
Vincent Bansaye
Keyword(s):  
Random Environment ◽  
Law Of Large Numbers ◽  
Branching Processes ◽  
Convergence In Distribution ◽  
Daughter Cells ◽  
State Dependent ◽  
Branching Model ◽  
Large Numbers ◽  
Dividing Cells ◽  
A Cell

We consider a branching model for a population of dividing cells infected by parasites. Each cell receives parasites by inheritance from its mother cell and independent contamination from outside the cell population. Parasites multiply randomly inside the cell and are shared randomly between the two daughter cells when the cell divides. The law governing the number of parasites which contaminate a given cell depends only on whether the cell is already infected or not. We first determine the asymptotic behavior of branching processes in a random environment with state-dependent immigration, which gives the convergence in distribution of the number of parasites in a cell line. We then derive a law of large numbers for the asymptotic proportions of cells with a given number of parasites. The main tools are branching processes in a random environment and laws of large numbers for a Markov tree.

scholarly journals Cell contamination and branching processes in a random environment with immigration

2009 ◽  
Vol 41 (04) ◽  
pp. 1059-1081
Author(s):  
Vincent Bansaye
Keyword(s):  
Random Environment ◽  
Law Of Large Numbers ◽  
Branching Processes ◽  
Convergence In Distribution ◽  
Daughter Cells ◽  
State Dependent ◽  
Branching Model ◽  
Large Numbers ◽  
Dividing Cells ◽  
A Cell

We consider a branching model for a population of dividing cells infected by parasites. Each cell receives parasites by inheritance from its mother cell and independent contamination from outside the cell population. Parasites multiply randomly inside the cell and are shared randomly between the two daughter cells when the cell divides. The law governing the number of parasites which contaminate a given cell depends only on whether the cell is already infected or not. We first determine the asymptotic behavior of branching processes in a random environment with state-dependent immigration, which gives the convergence in distribution of the number of parasites in a cell line. We then derive a law of large numbers for the asymptotic proportions of cells with a given number of parasites. The main tools are branching processes in a random environment and laws of large numbers for a Markov tree.

Bellman–Harris branching processes with state-dependent immigration

1985 ◽  
Vol 22 (04) ◽  
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.

scholarly journals On Uncertainty Relations and Entanglement Detection with Mutually Unbiased Measurements

2015 ◽  
Vol 22 (01) ◽  
pp. 1550005 ◽  
Author(s):  
Alexey E. Rastegin
Keyword(s):  
The State ◽  
Uncertainty Relations ◽  
Trade Off ◽  
Entropic Uncertainty Relations ◽  
Finite Dimensional ◽  
State Dependent ◽  
Entanglement Detection

We formulate some properties of a set of several mutually unbiased measurements. These properties are used for deriving entropic uncertainty relations. Applications of mutually unbiased measurements in entanglement detection are also revisited. First, we estimate from above the sum of the indices of coincidence for several mutually unbiased measurements. Further, we derive entropic uncertainty relations in terms of the Rényi and Tsallis entropies. Both the state-dependent and state-independent formulations are obtained. Using the two sets of local mutually unbiased measurements, a method of entanglement detection in bipartite finite-dimensional systems may be realized. A certain trade-off between a sensitivity of the scheme and its experimental complexity is discussed.

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