Rectification
PROBABILITY SEMINAR
DURHAM UNIVERSITY
On Friday 27 May there will be a probability seminar at Durham University.
Below you will find the programme and abstract. You are all welcome.
Location: Durham University, Department of Mathematical Sciences, CM221.
If you have any questions, please contact:
Pauline Coolen-Schrijner
[log in to unmask]
0191 3343073
PROGRAMME:
2.15 - 3.00 pm Dr A Chen (University of Greenwich)
Title: Uniqueness and extinction properties of weighted
collision branching processes
3.00 - 3.45 pm Dr D Clancy (University of Liverpool)
Title: Quasi-stationary distributions of some infection
models.
3.45 - 4.15 pm Tea
4.15 - 5.00 pm Dr EA van Doorn (University of Twente, The Netherlands)
Title: Birth-death processes with killing: Orthogonal
polynomials and quasi-stationary distributions.
ABSTRACTS:
Uniqueness and extinction properties of weighted collision branching
processes (Dr A Chen)
Different from the Markov branching process, the weighted collision
branching process is an interacting branching system. The basic properties
regarding uniqueness, extinction and explosion behaviour of such system are
addressed in this talk. It is proved that the super-explosive weighted
collision branching process is honest if and only if the mean death rate is
greater than or equal to the mean birth rate while the sub-explosive one is
almost honest. Explicit expressions for the extinction probability, the mean
and the conditional mean extinction times are presented. The explosion
behaviour of such interacting branching models is investigated and an
explicit expression for mean explosive time is established. It is revealed
that these basic properties are substantially different between the
super-explosive and sub-explosive weighted collision branching processes.
Quasi-stationary distributions of some infection models (Dr D Clancy)
I will briefly outline a stochastic ordering result for the classical SIS
(Susceptible - Infected - Susceptible) infection model. I will then
describe how the SIS model may be extended to incorporate indirect
transmission of infection via free-living infectious stages (eg
environmental bacteria). For the extended model I will discuss limiting
conditional distributions of interest, questions of existence, Normal
approximation, a simulation method using a piecewise-deterministic Markov
process approximation, and the effect of indirect transmission upon
persistence time of the infection.
Birth-death processes with killing: Orthogonal polynomials and
quasi-stationary distributions (Dr EA van Doorn)
The Karlin-McGregor representation for the transition probabilities of a
birth-death process with an absorbing bottom state involves a sequence of
orthogonal polynomials and the corresponding measure. This representation
can be generalized to a setting in which a transition to the absorbing state
(killing) is possible from any state rather than just one state. In the talk
I will discuss to what extent properties of birth-death processes, in
particular with regard to the existence and shape of quasi-stationary
distributions (initial distributions which are such that the state
distribution of the process, conditional on non-absorption, is constant over
time), remain valid in the generalized setting. It turns out that the
elegant structure of the theory of quasi-stationarity for birth-death
processes remains intact as long as killing is possible from only finitely
many states, but becomes more elaborate otherwise.
(The talk is based on joint work with P. Coolen-Schrijner and A. Zeifman.)
--
================================
Dr. P. Coolen-Schrijner
Dept. of Mathematical Sciences
University of Durham
Science Laboratories, South Road
Durham DH1 3LE, UK.
Tel: +44 (0) 191 334 3073
+44 (0) 191 334 3050 (secr.)
Fax: +44 (0) 191 334 3051
e-mail: [log in to unmask]
homepage: http://maths.dur.ac.uk/stats/people/ps/ps.html
|