Greven A (1986)
Publication Language: English
Publication Type: Book chapter / Article in edited volumes
Publication year: 1986
Publisher: Springer
Edited Volumes: Lecture Notes in Mathematics
City/Town: Berlin Heidelberg New York
Book Volume: 1212
Pages Range: 145-164
We consider a class of processes on (lli)S
modelling population
growth. The dynamics of the system consists of: motion of particles,
birth and death of individual particles, extinction of all particles
at a site and splitting of all particles at a site.
We investigate the changes in the longterm behaviour of these systems,
changes, which occur if we replace parameters of the evolution (as off-
spring distribution or site killing rate) by collections indexed by
the sites and generated by a random mechanism at time O.
We study the system for each (a.s.) realisation of the random environ-
ment and show that the exponential growth rate of the expected number
of particles per site (given the environment)depends heavily on the
character of the underlying motion; the growth rate is maximal (and
can be calculated explicitly) iff the underlying motion has no drift.
We propose an approach for the more detailed study of the asymptotic
behaviour (t+ oo ) of the process and show for Branching Random Walks a
law of large numbers, respectively convergence to a "Poisson limit".
Furthermore we show that nontrivial equilibria for our evolutions can
exist only in the case of a translation-invariant structure of the mean
offspring size and the mean death rates.
APA:
Greven, A. (1986). A class of infinite particle systems in random environment. In P- Tautu (Eds.), Lecture Notes in Mathematics. (pp. 145-164). Berlin Heidelberg New York: Springer.
MLA:
Greven, Andreas. "A class of infinite particle systems in random environment." Lecture Notes in Mathematics. Ed. P- Tautu, Berlin Heidelberg New York: Springer, 1986. 145-164.
BibTeX: Download