Birth-and-Death Process

2022 ◽  
pp. 129-140
Author(s):  
Olga Korosteleva
Keyword(s):  
Death Process ◽  
Birth And Death Process

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

A stochastic process related to language change

1970 ◽  
Vol 7 (01) ◽  
pp. 69-78 ◽  
Author(s):  
Barron Brainerd
Keyword(s):  
Stochastic Process ◽  
Language Change ◽  
Death Process ◽  
Birth And Death Process ◽  
Standard Methods

The purpose of this note is two-fold. First, to introduce the mathematical reader to a group of problems in the study of language change which has received little attention from mathematicians and probabilists. Secondly, to introduce a birth and death process, arising naturally out of this group of problems, which has received little attention in the literature. This process can be solved using the standard methods and the solution is exhibited here.

Multi-Location Inventory Model Considering Bidirectional and Unidirectional Transshipments Simultaneously

2013 ◽  
Vol 694-697 ◽  
pp. 2742-2745
Author(s):  
Jin Hong Zhong ◽  
Yun Zhou
Keyword(s):  
Process Model ◽  
Approximate Calculation ◽  
Inventory Model ◽  
Inventory System ◽  
Death Process ◽  
Birth And Death Process ◽  
Inventory Models ◽  
Continuous Review ◽  
Poisson Demand ◽  
Queue Theory

Abstract. A cross-regional multi-site inventory system with independent Poisson demand and continuous review (S-1,S) policy, in which there is bidirectional transshipment between the locations at the same area, and unidirectional transshipment between the locations at the different area. According to the M/G/S/S queue theory, birth and death process model and approximate calculation policy, we established inventory models respectively for the loss sales case and backorder case, and designed corresponding procedures to solve them. Finally, we verify the effectiveness of proposed models and methods by means of a lot of contrast experiments.

AN AGE-DEPENDENT BIRTH AND DEATH PROCESS

Biometrika ◽  
1955 ◽  
Vol 42 (3-4) ◽  
pp. 291-306 ◽  
Author(s):  
W. A. O'N WAUGH
Keyword(s):  
Death Process ◽  
Birth And Death Process ◽  
Age Dependent

On a property of finite-state birth and death processes

1986 ◽  
Vol 23 (04) ◽  
pp. 859-866
Author(s):  
A. J. Branford
Keyword(s):  
Simple Proof ◽  
Death Process ◽  
Birth And Death Process ◽  
Birth And Death Processes ◽  
Converse Result ◽  
Finite State ◽  
Event Times

A simple proof is given of the result that the ‘overflow' from a finite-state birth and death process is a renewal stream characterized by hyperexponential inter-event times. Our structure is utilized to give a converse result that any hyperexponential renewal stream can be so produced as the overflow from a finite-state birth and death process.

A stochastic model for two interacting populations

1970 ◽  
Vol 7 (3) ◽  
pp. 544-564 ◽  
Author(s):  
Niels G. Becker
Keyword(s):  
Stochastic Model ◽  
Linear Models ◽  
Death Process ◽  
Linear Component ◽  
Birth And Death Process ◽  
Linear Interaction ◽  
Interacting Populations ◽  
Non Linear ◽  
The Subject ◽  
Interaction Component

To explain the growth of interacting populations, non-linear models need to be proposed and it is this non-linearity which proves to be most awkward in attempts at solving the resulting differential equations. A model with a particular non-linear component, initially proposed by Weiss (1965) for the spread of a carrier-borne epidemic, was solved completely by different methods by Dietz (1966) and Downton (1967). Immigration parameters were added to the model of Weiss and the resulting model was made the subject of a paper by Dietz and Downton (1968). It is the aim here to further generalize the model by introducing birth and death parameters so that the result is a linear birth and death process with immigration for each population plus the non-linear interaction component.

Nucleation rates and the kinetics of particle growth II. The birth and death process

1964 ◽  
Vol 277 (1369) ◽  
pp. 167-182 ◽  
Keyword(s):  
Steady State ◽  
Homogeneous Nucleation ◽  
Time Lag ◽  
Particle Growth ◽  
Statistical Problem ◽  
Death Process ◽  
Birth And Death Process ◽  
Growth Mechanisms ◽  
Nucleation Kinetics ◽  
Kinetics Of

The model considered in part I is generalized to include growth mechanisms in which the chemical reaction which proceeds at the particle-atm osphere interface is reversible, so that molecules may evaporate from a particle as well as condense upon it. The Becker-Döring-Zeldovich-Frenkel theory of homogeneous nucleation kinetics is then reviewed in the light of the known statistical problem of the birth -and -death process, and an improved approximation is introduced which significantly alters the calculated results. Both steady-state nucleation kinetics and the time lag problem are discussed.

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