Analysis of transient behaviour of certain processes with return to a central state

1983 ◽  
Vol 20 (1) ◽  
pp. 61-70 ◽  
Author(s):  
Peter G. Buckholtz ◽  
L. Lorne Campbell ◽  
Ross D. Milbourne ◽  
M. T. Wasan
Keyword(s):  
Probability Distribution ◽  
Diffusion Equation ◽  
Diffusion Approximation ◽  
Cash Management ◽  
Central State ◽  
Transient Behaviour ◽  
Management Problems ◽  
Transient Probability ◽  
Birth Death

In economics, cash management problems may be modelled by birth-death processes which reset to central states when a boundary is reached. The nature of the transient behaviour of the probability distribution of such processes symmetric about a central state is investigated. A diffusion approximation of such processes is given and the transient probability behaviour derived from the diffusion equation.

Analysis of transient behaviour of certain processes with return to a central state

1983 ◽  
Vol 20 (01) ◽  
pp. 61-70
Author(s):  
Peter G. Buckholtz ◽  
L. Lorne Campbell ◽  
Ross D. Milbourne ◽  
M. T. Wasan
Keyword(s):  
Probability Distribution ◽  
Diffusion Equation ◽  
Diffusion Approximation ◽  
Cash Management ◽  
Central State ◽  
Transient Behaviour ◽  
Management Problems ◽  
Transient Probability ◽  
Birth Death

In economics, cash management problems may be modelled by birth-death processes which reset to central states when a boundary is reached. The nature of the transient behaviour of the probability distribution of such processes symmetric about a central state is investigated. A diffusion approximation of such processes is given and the transient probability behaviour derived from the diffusion equation.

A Multilevel birth-death particle system and its continuous diffusion

1993 ◽  
Vol 25 (03) ◽  
pp. 549-569 ◽  
Author(s):  
Yadong Wu
Keyword(s):  
Diffusion Process ◽  
Unique Solution ◽  
Diffusion Approximation ◽  
Particle System ◽  
Martingale Problem ◽  
The Moment ◽  
Birth Death

In this paper we introduce a multilevel birth-death particle system and consider its diffusion approximation which can be characterized as aM([R+)-valued process. The tightness of rescaled processes is proved and we show that the limitingM(R+)-valued process is the unique solution of theM([R+)-valued martingale problem for the limiting generator. We also study the moment structures of the limiting diffusion process.

A bivariate birth-death process which approximates to the spread of a disease involving a vector

1972 ◽  
Vol 9 (01) ◽  
pp. 65-75 ◽  
Author(s):  
D. A. Griffiths
Keyword(s):  
Simple Model ◽  
Probability Distribution ◽  
General Class ◽  
Large Population ◽  
Vector Model ◽  
Death Process ◽  
The Mean ◽  
Probability Of Extinction ◽  
Over Time ◽  
Birth Death

A simple model for a bivariate birth-death process is proposed. This model approximates to the host-vector epidemic situation. An investigation of the transient process is made and the mean behaviour over time is explicitly found. The probability of extinction and the behaviour of the process conditional upon extinction are examined and the probability distribution of the cumulative population size to extinction is found. Appropriate circumstances are suggested under which the model might possibly be applied to malaria. The host-vector model is classified within a general class of models which represent large population approximations to epidemics involving two types of infectives.

A bivariate birth-death process which approximates to the spread of a disease involving a vector

1972 ◽  
Vol 9 (1) ◽  
pp. 65-75 ◽  
Author(s):  
D. A. Griffiths
Keyword(s):  
Simple Model ◽  
Probability Distribution ◽  
General Class ◽  
Large Population ◽  
Vector Model ◽  
Death Process ◽  
The Mean ◽  
Probability Of Extinction ◽  
Over Time ◽  
Birth Death

A simple model for a bivariate birth-death process is proposed. This model approximates to the host-vector epidemic situation. An investigation of the transient process is made and the mean behaviour over time is explicitly found. The probability of extinction and the behaviour of the process conditional upon extinction are examined and the probability distribution of the cumulative population size to extinction is found. Appropriate circumstances are suggested under which the model might possibly be applied to malaria. The host-vector model is classified within a general class of models which represent large population approximations to epidemics involving two types of infectives.

scholarly journals Diffusion approximation for a Knudsen gas in a thin domain with reflexive chaotic law

2001 ◽  
Vol 63 (3) ◽  
pp. 497-514 ◽  
Author(s):  
Christian Dogbé
Keyword(s):  
Diffusion Equation ◽  
Diffusion Approximation ◽  
Anisotropic Diffusion ◽  
Gas Flow ◽  
Thin Domain ◽  
Norm Topology ◽  
Arnold’S Cat Map ◽  
Limiting Behaviour ◽  
Anisotropic Diffusion Equation ◽  
Knudsen Gas

This paper treats a rarefied Knudsen gas flow between two infinite plates, with boundary reflexion ruled by a reflexive chaotic law called “Arnold's cat map”. It is shown that the limiting behaviour, when the distance between the plates goes to 0, is described by an (anisotropic) diffusion equation in the norm topology.

Sign in / Sign up

Export Citation Format

Share Document