
Report on MASCOS Workshop on Markov Chains
The University of Queensland
Monday 4th April 2005
General
Markov chains are the simplest mathematical models for
random phenomena
that evolve over time. Their structure is sufficiently simple that one
can say a great deal about their behaviour, yet, at the same time, the
class of Markov chains is rich enough to serve in many applications.
Indeed, Markov chains are the first and most important examples of
stochastic models which arise in areas as diverse as population
biology, chemical kinetics and telecommunications.
This workshop, sponsored by the ARC Centre of Excellence
for Mathematics and Statistics of Complex Systems (MASCOS), brought together
practitioners and mathematicians to examine recent
developments in the theory and applications Markov chains.
Invited speakers
 Anyue Chen (University of Greenwich)
 Tony Pakes (University of Western Australia)
 Phil Pollett (MASCOS, University of Queensland)
 David Sirl (MASCOS, University of Queensland)
 Hanjun Zhang (MASCOS, University of Queensland)
[There were no contributed papers]
Venue
Seminar Rooms 1 and 2,
Emmanuel College,
St Lucia Campus, University of Queensland.
Organizers
David Sirl and Phil Pollett (MASCOS, University of
Queensland)
Programme

09:15 
Registration 

09:30 
David Sirl 
Markov chains: an introduction/review 

10:30 
Break 
[Refeshments provided] 

11:00 
Hanjun Zhang 
Quasistationary distributions and the decay parameter 

12:00 
Tony Pakes 
Longrange Markovian dependence 

13:00 
Lunch Break 
[Lunch provided] 

14:00 
Anyue Chen 
Uniqueness, extinction, and explosion properties of the Weighted
Collision
Branching Process


15:00 
Break 
[Refeshments provided] 

15:30 
Phil Pollett 
Which Markov chains have a given invariant measure?


16:30 
Close 
Abstracts
 Anyue Chen
Uniqueness, extinction and explosion properties of the
Weighted Collision
Branching Process
Abstract: The basic questions of uniqueness, extinction
and explosivity of one
kind of interacting branching system, the Weighted Collision Branching
Process (WCBP), are addressed in this talk. It is proved that in the
superexplosive case, the process is honest if and only if the mean
death rate is greater than or equal to the mean birth rate, while,
in the subexplosive case, it is always honest. Explicit expressions
for the extinction probability, and the mean and the conditional mean
extinction times are presented. Explosivity of the WCBP is investigated
and an explicit expression for mean explosion time is established.
We shall see that the superexplosive and the subexplosive WCBPs
exhibit substantially different behaviour.
[This is joint work with Junping Li, Phil Pollett and Hanjun Zhang.]
 Tony Pakes
Longrange Markovian dependence
Abstract: The title is a tease in that it alludes to
geographical longrange
influences on two topics I will address. The first of these relates to
the fact, shown by Darlington and Pollett, that if a Markov process
has an absorbing state which it hits with probability less than one,
then any limiting conditional law is not quasistationary.
Nevertheless,
there is some nice theory for this situation. I will discuss it,
together
with an illustration. The second topic is about a uniqueness question
for nonlinear (i.e. weighted) Markov branching processes which arose
first from a remark made electronically to me by Anyue Chen.
 Phil Pollett
Which Markov chains have a given invariant measure?
Abstract: I will consider the following problem: given a
stable, conservative
qmatrix Q of transition rates over a denumerable statespace S,
together with a subinvariant measure m for Q, determine all Qprocesses
for which m is an invariant measure. I will review recent work on
this problem, giving particular attention to the case when Q is a
singleexit qmatrix. I will also examine the case
when S consists of
a single absorbing state 0 and an irreducible class C, and consider the
problem of constructing Qprocesses for which a given measure m is minvariant on C.
[The latter is joint work with Hanjun Zhang.]
[talk]
 David Sirl
Markov chains: an introduction/review
Abstract: I will give a brief account of the theory of
Markov chains, from
discrete time, finite statespace to continuous time, countable state
processes. I will recall various quantities of interest, including
hitting
probabilities, expected hitting times, and stationary and
quasistationary
distributions, and illustrate these concepts with numerous examples.
[talk]
 Hanjun Zhang
Quasistationary distributions and the decay parameter
Abstract: The existence of quasistationary distributions
(qsds) is addressed in
this talk. I will review some work on this problem and present some new
results. The decay parameter, which is closely related to qsds, will be
discussed. I will give a sufficient condition for the decay parameter
to be positive for a general Markov chain.
[talk]
Participants

Name 
Email 
Affiliation 





Moshin Ali 
moshin at itee.uq.edu.au 
School of Information Technology and Electrical
Engineering, University of Queensland 

John Paul Barjaktarevic 
jpb at physics.uq.edu.au 
Department of Physics, University of Queensland 

Kevin Burrage 
kb at maths.uq.edu.au 
Advanced Computational Modelling Centre, University of
Queensland 

Ben Cairns 
bjc at maths.uq.edu.au 
MASCOS, University of Queensland 

Anyue Chen 
A.Chen at gre.ac.uk 
Mathematical Sciences Department, University of
Greenwich 

Zhao Yang Dong 
zdong at itee.uq.edu.au 
School of Information Technology and Electrical
Engineering, University of Queensland 

Selina Fothergill 
selinafo at psy.uq.edu.au 
Key Centre for Applied Cognitive Psychology and Human
Factors, University of Queensland 

Marcus Gallagher 
marcusg at itee.uq.edu.au 
School of Information Technology and Electrical
Engineering, University of Queensland 

Ben Gladwin 
gladwin at maths.uq.edu.au 
MASCOS, University of Queensland 

Andrei Hryshko 
dushenka at itee.uq.edu.au 
School of Information Technology and Electrical
Engineering, University of Queensland 

Naveen Kumar 
naveen at itee.uq.edu.au 
School of Information Technology and Electrical
Engineering, University of Queensland 

Dharma Lesmono 
dlesmono at maths.uq.edu.au 
MASCOS, University of Queensland 

Ariel Liebman 
aliebman at itee.uq.edu.au 
ARC Centre for Complex Systems, University of Queensland 

Valerie Lim 
lim at itee.uq.edu.au 
School of Information Technology and Electrical
Engineering, University of Queensland 

Miao (Jennie) Lu 
lumiao at itee.uq.edu.au 
School of Information Technology and Electrical
Engineering, University of Queensland 

Stefan Maetschke 
stefan at itee.uq.edu.au 
School of Information Technology and Electrical
Engineering, University of Queensland 

Marissa McBride 
s4033977 at student.uq.edu.au 
Department of Mathematics, University of Queensland 

Rizah Memisevic 
r.memisevic at uq.edu.au 
Key Centre for Applied Cognitive Psychology and Human
Factors, University of Queensland 

Sho Nariai 
sho at maths.uq.edu.au 
Department of Mathematics, University of Queensland 

Michael Nielsen 
nielsen at physics.uq.edu.au 
Department of Physics, University of Queensland 

Tony Pakes 
pakes at maths.uwa.edu.au 
School of Mathematics and Statistics, University of
Western Australia 

Phil Pollett 
pkp at maths.uq.edu.au 
MASCOS, University of Queensland 

Tony Roberts 
apr at maths.uq.edu.au 
Department of Mathematics, University of Queensland 

Joshua Ross 
jvr at maths.uq.edu.au 
MASCOS, University of Queensland 

Asrul Sani 
asani at maths.uq.edu.au 
Department of Mathematics, University of Queensland 

Mark Seeto 
mbs at maths.uq.edu.au 
Department of Mathematics, University of Queensland 

David Sirl 
dsirl at maths.uq.edu.au 
MASCOS, University of Queensland 

Antony Stace 
aws at maths.uq.edu.au 
MASCOS, University of Queensland 

Thomas Taimre 
ttaimre at maths.uq.edu.au 
MASCOS, University of Queensland 

Bill Whiten 
W.Whiten at uq.edu.au 
Julius Kruttschnitt Mineral Research Centre, University
of Queensland 

Andy Wilkins 
awilkins at maths.uq.edu.au 
Department of Mathematics, University of Queensland 

Burton Wu 
burton.wu at team.telstra.com 


George (Zhao) Xu 
xuzhao at itee.uq.edu.au 
School of Information Technology and Electrical
Engineering, University of Queensland 

WenLi Yang 
wenli at maths.uq.edu.au 
Department of Mathematics, University of Queensland 

Hanjun Zhang 
hjz at maths.uq.edu.au 
MASCOS, University of Queensland 

Lu Zhe 
luzhe at itee.uq.edu.au 
School of Information Technology and Electrical
Engineering, University of Queensland 

Justin Zhu 
j.zhu at imb.uq.edu.au 
Institute for Molecular Bioscience, University of
Queensland 
