Some Estimates for a One-Dimensional Birth and Death Process in a Random Environment

1992 ◽  
Vol 36 (3) ◽  
pp. 578-583 ◽  
Author(s):  
A. A. Butov
Keyword(s):  
Random Environment ◽  
Death Process ◽  
Birth And Death Process ◽  
One Dimensional

Birth and death processes with random environments in continuous time

1981 ◽  
Vol 18 (01) ◽  
pp. 19-30 ◽  
Author(s):  
Robert Cogburn ◽  
William C. Torrez
Keyword(s):  
Discrete Time ◽  
Random Environment ◽  
Continuous Time ◽  
Death Process ◽  
Random Environments ◽  
Birth And Death Process ◽  
Time Model ◽  
Birth And Death Processes ◽  
Discrete Time Model ◽  
Extinction Probabilities

A generalization to continuous time is given for a discrete-time model of a birth and death process in a random environment. Some important properties of this process in the continuous-time setting are stated and proved including instability and extinction conditions, and when suitable absorbing barriers have been defined, methods are given for the calculation of extinction probabilities and the expected duration of the process.

scholarly journals Birth and death processes in randomly fluctuating environments

2002 ◽  
Vol 166 ◽  
pp. 93-115
Author(s):  
Kanji Ichihara
Keyword(s):  
Random Environment ◽  
Time Dependent ◽  
Death Process ◽  
Birth And Death Process ◽  
Birth And Death Processes ◽  
Fluctuating Environments

AbstractA birth and death process in a time-dependent random environment is introduced. We will discuss the recurrence and transience properties for the process.

Quasi-stationary distributions and one-dimensional circuit-switched networks

1987 ◽  
Vol 24 (04) ◽  
pp. 965-977 ◽  
Author(s):  
Ilze Ziedins
Keyword(s):  
Communication Networks ◽  
Stationary Distribution ◽  
Death Process ◽  
Birth And Death Process ◽  
Stationary Distributions ◽  
Switched Networks ◽  
One Dimensional ◽  
Special Cases ◽  
Quasi Stationary Distribution

We discuss the quasi-stationary distribution obtained when a simple birth and death process is conditioned on never exceeding K. An application of this model to one-dimensional circuit-switched communication networks is described, and some special cases examined.

Quasi-stationary distributions and one-dimensional circuit-switched networks

1987 ◽  
Vol 24 (4) ◽  
pp. 965-977 ◽  
Author(s):  
Ilze Ziedins
Keyword(s):  
Communication Networks ◽  
Stationary Distribution ◽  
Death Process ◽  
Birth And Death Process ◽  
Stationary Distributions ◽  
Switched Networks ◽  
One Dimensional ◽  
Special Cases ◽  
Quasi Stationary Distribution

We discuss the quasi-stationary distribution obtained when a simple birth and death process is conditioned on never exceeding K. An application of this model to one-dimensional circuit-switched communication networks is described, and some special cases examined.

Birth and death processes with random environments in continuous time

1981 ◽  
Vol 18 (1) ◽  
pp. 19-30 ◽  
Author(s):  
Robert Cogburn ◽  
William C. Torrez
Keyword(s):  
Discrete Time ◽  
Random Environment ◽  
Continuous Time ◽  
Death Process ◽  
Random Environments ◽  
Birth And Death Process ◽  
Time Model ◽  
Birth And Death Processes ◽  
Discrete Time Model ◽  
Extinction Probabilities

A generalization to continuous time is given for a discrete-time model of a birth and death process in a random environment. Some important properties of this process in the continuous-time setting are stated and proved including instability and extinction conditions, and when suitable absorbing barriers have been defined, methods are given for the calculation of extinction probabilities and the expected duration of the process.

A continuous-time analogue of random walk in a random environment

1980 ◽  
Vol 17 (1) ◽  
pp. 259-264 ◽  
Author(s):  
Grant Ritter
Keyword(s):  
Random Walk ◽  
Random Environment ◽  
Continuous Time ◽  
Random Variables ◽  
Death Process ◽  
Birth And Death Process ◽  
Time Parameters

By making the time parameters of a birth and death process random variables, we create a continuous-time analogue of random walk in a random environment. Criteria for recurrence or transience are discussed and an a.s. convergence law is determined.

Interparticle dependence in a linear death process subjected to a random environment

1990 ◽  
Vol 27 (3) ◽  
pp. 491-498 ◽  
Author(s):  
Claude Lefèvre ◽  
György Michaletzky
Keyword(s):  
Random Environment ◽  
Death Rate ◽  
Monotone Function ◽  
Death Process ◽  
Birth And Death Process ◽  
Survival Times ◽  
Current State ◽  
Non Linear

Recently, Ball and Donnelly (1987) investigated the nature of the interparticle dependence in a death process with non-linear rates. In this note, after some remarks on their result, a similar problem is examined for a linear death process where the death rate per particle is a monotone function of the current state of a random environment. It is proved that if the exterior process involved is a homogeneous birth-and-death process valued in ℕ, then the survival times of any subset of particles are positively upper orthant dependent. A simple example shows that this property is not valid for general exterior processes.

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