Phil Pollett's Research Pages

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ARC Funded Projects

Papers and Abstracts

* Analytical and Computational Methods for Modelling
Evanescent Random Processes *
(1992-1994) and (1995-1997)

Published work

Agliardi, E. and Bebbington, M.S. (1997)
Self-reinforcing mechanisms and market information.
*European Journal of Operational Research* 96, 444-454.

Bebbington. M.S. (1995)
Evaluating quasistationary behaviour of epidemic
models by means of parallel aggregation / disaggregation.
In (Eds P. Binning, H. Bridgman and B. Williams),
*Proceedings of the International Congress on Modelling
and Simulation 1995*,
Modelling and Simulation Society of Australia, Newcastle, Vol. 2,
pp. 203-208.

Bebbington, M.S. (1997)
A hierarchical stress-release model for synthetic seismicity.
*Journal of Geophysical Research-Solid Earth* 102, 11677-11687.

Bebbington, M.S. (1997)
Parallel implementation of an aggregation/disaggregation method for
evaluating quasi-stationary behaviour in continuous-time Markov chains.
*Parallel Computing* 23, 1545-1559.

Bebbington, M.S., Pollett, P.K., Singer, D. and Ziedins, I. (1993)
Approximate models for a symmetric circuit-switched
network with one and two link traffic.
* Technical Report*, Discipline of Mathematics, The University of
Queensland.

Bebbington, M.S., Pollett, P.K. and Zheng, X. (1995)
Dual constructions for pure-jump Markov processes.
* Markov Processes and Related Fields* 1, 513-558.

Breyer, L.A. and Hart, A.G. (1996)
Approximations of quasistationary distributions for Markov chains.
In (Eds Richard J. Wilson, D.N. Pra Murthy and Shunji Osaki)
* Proceedings of the 2nd Australia-Japan Workshop on Stochastic Models
in Engineering, Technology and Management*,
Technology Management Centre, The University of Queensland, pp. 81-90.

Breyer, L.A. and Hart, A.G. (1998)
Approximations of quasistationary distributions for Markov chains.
*Mathematical and Computer Modelling* 31, 69-79.

O'Cinneide, C.A. (1999)
Phase-type distributions: open problems and a few properties.
*Stochastic Models* 15, 731-757.

O'Cinneide, C.A., and Pokrovskii, A.V. (2000)
Nonuniform random transformations.
*The Annals of Applied Probabability* 10, 1151-1181.

Coolen-Schrijner, P., Hart, A.G. and Pollett, P.K.
(2000)
Quasistationarity of continuous-time Markov chains with positive drift.
*Journal of the Australian Mathematical Society, Series B* 41,
423-441.

Coolen-Schrijner, P. and Pollett, P.K.
(1999)
Quasi-stationarity of discrete-time Markov chains with drift to
infinity.
*Methodology and Computing in Applied Probability* 1,
81-96.

Darlington, S.J. and Pollett, P.K. (2000)
Quasistationarity in continuous time Markov chains
where absorption is not certain.
* Journal of Applied Probability* 37, 598-600.

Elmes, S., Pollett, P.K. and Walker, D. (1996)
On the relationship between mu-invariant
measures and quasistationary distributions for absorbing continuous-time
Markov chains when absorption is not certain.
In (Eds Richard J. Wilson, D.N. Pra Murthy and Shunji Osaki)
* Proceedings of the 2nd Australia-Japan Workshop on Stochastic Models
in Engineering, Technology and Management*,
Technology Management Centre, The University of Queensland, pp. 131-140.

Elmes, S., Pollett, P.K. and Walker, D. (1998)
Further results on
the relationship between mu-invariant
measures and quasistationary distributions for absorbing continuous-time
Markov chains.
* Mathematical and Computer Modelling* 31, 107-113.

Hambly, B.M. and Jones, O.D. (1998)
Modelling transport in disordered media via diffusion on fractals.
* Mathematical and Computer Modelling* 31, 129-142.

Hart, A.G. and Pollett, P.K. (1996)
Direct analytical methods for determining quasistationary
distributions for continuous-time Markov chains. In
(Eds C.C. Heyde, Yu V. Prohorov, R. Pyke and S.T. Rachev)
*Athens Conference on Applied
Probability and Time Series Analysis, Volume I: Applied Probability, In
Honour of J.M. Gani*,
Lecture Notes in Statistics 114,
Springer-Verlag, New York, pp. 116-126.

Hart, A.G. and Pollett, P.K. (1996)
New methods for determining quasistationary
distributions for continuous-time Markov chains.
In (Eds Richard J. Wilson, D.N. Pra Murthy and Shunji Osaki)
* Proceedings of the 2nd Australia-Japan Workshop on Stochastic Models
in Engineering, Technology and Management*,
Technology Management Centre, The University of Queensland, pp. 177-186.

Hart, A.G. and Pollett, P.K. (1998)
New methods for determining quasistationary
distributions for continuous-time Markov chains.
* Mathematical and Computer Modelling* 31, 143-150.

Jones, O.D. (1996)
Stochastic models for diffusion in disordered media using fractals.
In (Eds Richard J. Wilson, D.N. Pra Murthy and Shunji Osaki)

Jones, O.D. (1997)
On the convergence of multi-type branching processes with varying
environments. *Annals of Applied Probability* 7, 772-801.

Jones, O.D. (1999)
Continuity for multi-type branching processes with varying environments.
*Journal of Applied Probability* 36, 139-145.

Kijima, M., Nair, M.G., Pollett, P.K. and van Doorn, E. (1997)
Limiting conditional distributions for birth-death processes.
* Advances in Applied Probability* 29, 185-204.

Pollett, P.K. (1992)
Modelling random fluctuations in a bistable telecommunications network.
In (Ed W. Henderson)
* Proceedings of the 7th Australian Teletraffic Research Seminar*,
Teletraffic Research Centre, University of Adelaide,
Adelaide,
pp. 335-345.

Pollett, P.K. (1993)
Modelling the long-term behaviour of evanescent ecological systems.
In (Ed M. McAleer)
* Proceedings of the International Congress on Modelling
and Simulation*,
Modelling and Simulation Society of Australia, Perth,
Vol. 1, pp. 157-162.

Pollett, P.K. (1993)
Recent advances in the theory and application of
quasistationary distributions.
In (Eds S. Osaki and D.N.P. Murthy)
* Proceedings of the Australia-Japan Workshop on Stochastic Models
in Engineering, Technology and Management*,
World Scientific,
Singapore,
pp. 477-486.

Pollett, P.K. (1993)
Analytical and computational methods for modelling the long-term
behaviour of evanescent random processes.
In (Eds D.J. Sutton, C.E.M. Pearce and E.A. Cousins)
* Decision Sciences: Tools for Today,
Proceedings of the 12th National Conference of the Australian
Society for Operations Research*,
Australian Society for Operations Research, Adelaide,
pp. 514-535.

Pollett, P.K. (1993)
Some comments on
``Optimal algorithms for minimal perfect hashing'' by
G. Havas and B.S. Majewski.
* Technical Report*,
Discipline of Mathematics, The University of Queensland.

Pollett, P.K. (1994)
On the identification of continuous-time Markov chains with
a given invariant measure.
* Journal of Applied Probability* 31, 897-910.

Pollett, P.K. (1995)
The determination of quasistationary distributions directly
from the transition rates of an absorbing Markov chain.
* Mathematical and Computer Modelling * ** 22**, 279-287.

Pollett, P.K. (1996)
Modelling the long-term behaviour of evanescent ecological systems.
* Ecological Modelling* 86, 135-139.

Pollett, P.K. (1997)
Limiting conditional distributions for stochastic metapopulation models.
In (Eds A.D. McDonald and M. McAleer)
* Proceedings of the International Congress on Modelling and Simulation*,
Vol. 2 (ISBN 0-86422-826-0),
Modelling and Simulation Society of Australia, Hobart, Australia, pp. 807-812.

Pollett, P.K. (1999)
Quasistationary distributions for continuous time Markov chains when absorption is not certain.
* Journal of Applied Probability* 36, 268-272.

Pollett, P.K. (1999)
Modelling quasi-stationary behaviour in metapopulations.
* Mathematics and Computers in Simulation* 47, 393-405.

Pollett, P.K. and Stewart, D.E. (1994)
An efficient procedure for computing quasistationary distributions
of Markov chains with sparse transition structure.
* Advances in Applied Probability* 26, 68-79.

Pollett, P.K. and Taylor, P.G. (1993)
On the problem of establishing the existence of
stationary distributions for continuous-time Markov chains.
* Probability in the Engineering and Informational Sciences* 7,
529-543.

Roberts, G.O., Jacka, S.D. and Pollett, P.K. (1997)
Non-explosivity of limits of conditioned birth and death processes.
* Journal of Applied Probability* 34, 35-45.

Stewart, D.E. and Bebbington, M.S. (1996)
An iterative aggregation / disaggregation procedure for modelling the
long-term behaviour of continuous-time evanescent random processes.
*Journal of Statistical Computation and Simulation* 56,
77-95.

Walker, D.M. (1998)
The expected time until absorption when absorption is not certain.
* Journal of Applied Probability* 35, 812-823.

Pollett, P.K., Analytical and computational methods for modelling
evanescent random processes, *The Oberwolfach Applied Probability
Meeting*, Mathematisches Forschungsinstitut Oberwolfach,
December 5-9, 1994.

Pollett, P.K.,
Analytical and computational methods for modelling evanescent
random processes.
*International Conference on Applied Probability and Time Series
Analysis*, Athens, Greece, March 22-26, 1995.

Pollett, P.K.,
Poisson approximations for telecommunications networks.
*International Meeting on Applied Probability* (Numazu'95),
Numazu, Japan, July 9-13, 1995.

Pollett, P.K.,
Modelling bistability in telecommunications networks.
*32nd Australasian Applied Mathematics Conference*
(ANZIAM'96),
Masterton, New Zealand, February 4-8, 1996.

Pollett, P.K.,
Estimating blocking probabilities in telecommunications networks
with linear structure.
*Sydney International Statistical Congress*,
Sydney, Australia, July 8-12, 1996.

Pollett, P.K.,
Modelling random fluctuations in a bistable telecommunications network.
*Stochastic Networks Workshop*
(Sydney International Statistical Congress satellite event),
Sydney, Australia, July 13, 1996.

Pollett, P.K.,
Quasistationarity in Markovian models.
*3rd International Symposium on Probability and its Applications*, Park
City, Utah, USA, July 30-August 1, 1997.

Pollett, P.K.,
Quasistationarity of continuous-time Markov chains with positive drift.
*The Oberwolfach Applied Probability Meeting*, Mathematisches
Forschungsinstitut Oberwolfach, Germany, November 29-December 5, 1998.

Bebbington, M., Multigrid methods for evaluating quasistationary
distributions for continuous-time Markov chains, *Weekend Conference
of the Queensland Branch of the Australian Mathematical Society
(Division of Applied Mathematics)*, Stewarts Hotel, Alexandra
Headlands, September, 1993.

Pollett, P.K., Computational methods for evaluating quasistationary
distributions, *11th Australian Statistical Conference*, Perth,
July, 1992.

Pollett, P.K., Computational methods for evaluating quasistationary
distributions, *20th European Meeting of Statisticians*, Bath,
September 1992.

Pollett, P.K., Modelling random fluctuations in a bistable
telecommunications network, *7th Australian Teletraffic Research
Seminar*, Murray Bridge, December 1992.

Pollett, P.K., Recent advances in the theory and application of
quasistationary distributions, *Weekend Conference of the Queensland
Branch of the Australian Mathematical Society (Division of Applied
Mathematics)*, Stewarts Hotel, Alexandra Headlands, September 1993.

Pollett, P.K.,
Acyclicity in random graphs,
*Workshop on Geometry and Discrete Mathematics*,
Queensland, Australia, November 4-7, 1995.

Hart, A.G.,
Quasistationary distributions for continuous-time Markov chains.
*23rd Conference on Stochastic Processes and their Applications*,
Singapore, June 1995.

Hart, A.G.,
The problem of truncation approximation in continuous-time Markov
chains.
*Australia/New Zealand Applied Probability Workshop*,
Second Valley, South
Australia, September 28-October 2, 1997.

Pollett, P.K.,
Quasistationarity in Markov chains with drift to infinity.
*Australia/New Zealand Applied Probability Workshop*,
Second Valley, South
Australia, September 28-October 2, 1997.

Pollett, P.K.,
Limiting conditional distributions for stochastic metapopulation models.
*Congress on Modelling and Simulation* (MODSIM'97), Hobart,
Australia,
December 8-11, 1997.

Singer, D., *RINGNET*,
a circuit-switching network simulation
package designed to simulate networks with a ring-like topology.

If you have any comments on these pages,

feel free to e-mail
me: * pkp@maths.uq.edu.au *