Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-13T00:42:17.734Z Has data issue: false hasContentIssue false

Spatial birth and death processes

Published online by Cambridge University Press:  01 July 2016

Chris Preston*
Affiliation:
Brasenose College, Oxford.

Extract

We examine birth and death processes where the birth/death rates depend on the particular configuration of the population. The easiest case is when the configurations form the subsets of some finite lattice (thus the state space is finite). In this case we look at the relationships between time-reversibility, nearest neighbour interactions, and the equilibrium state being a Markov random field. A more interesting case is when the entities which can be born or die can do so at any point in some bounded region of space (or the plane). This gives us a pure jump process, whose general properties are well-known, (see for example, Feller (1966) Vol. II Chapter X.3). We examine some particular examples and compute equilibrium distributions.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1975 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Spitzer, F. (1970) Interaction of Markov processes. Adv. in Maths 5, 246290.CrossRefGoogle Scholar
Feller, W. (1966) An Introduction to Probability Theory and its Applications, Wiley, New York.Google Scholar