Phil Pollett's Research Pages

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Papers and Abstracts

* Analytical and Computational Methods for Studying Explosive Random
Processes*
(2001-2003)

All published papers have been categorized according to the DEST classification, the main ones being B1= book chapter-research, C1= article in scholarly refereed journal, C5= edited volume of a refereed journal, E1= full written paper in a refereed conference proceedings, and E2= full written paper in an edited conference proceedings.

Some have been annotated with an "MR" reference.
This indicates the volume of *Mathematical Reviews*
(and then the location within that volume)
where a review of the paper can be found.

Journal articles (refereed) (C1)

Cairns, B.J. and Pollett, P.K. (2004)
Extinction times for a general birth, death and catastrophe
process.
*Journal of Applied Probability* 41, 1211-1218.
[MR 2005m:60165]

Cairns, B.J. and Pollett, P.K. (2005)
Approximating measures of persistence in a general class of population
processes.
*Theoretical Population Biology* 68, 77-90.

Chen, A. (2001)
Applications of Feller-Reuter-Riley transition functions.
*Journal of Mathematical Analysis and Applications* 260,
439-456.
[MR 2002f:60147]

Chen, A. (2002)
Ergodicity and stability of generalised Markov branching
processes with resurrection.
*Journal of Applied Probability* 39, 786-803.
[MR 2003m:60206]

Chen, A. (2002) Uniqueness and extinction properties of generalised Markov branching processes. Journal of Mathematical Analysis and Applications 274, 482-494. [MR 2003h:60124]

Chen, A. and Liu, K. (2002)
Piecewise birth-death processes.
*Markov Processes and Related Fields* 8, 665-698.
[MR 2003k:60208]

Chen, A. and Liu, K. (2003)
Birth-death processes with an instantaneous reflection barrier.
*Journal of Applied Probability* 39, 163-179.
[MR 2003k:60209]

Chen, A. and Renshaw, E. (2004)
Markovian bulk-arriving queues with state-dependent control and idle time.
*Advances in Applied Probability* 36, 499-524.
[MR 2005b:60199]

Chen, A., Zhang, H. and Hou, Z. (2002)
Feller transition functions, resolvent decomposition theorems, and their
application in unstable denumerable Markov processes.
In (Eds Zhenting Hou, Jerzy A. Filar and Anyue Chen)
*Markov Processes and Controlled Markov Chains*, Kluwer, pp. 15-39.
[MR 2004k:60209]

Chen, A., Zhang, H., Liu, K. and Rennolls, K. (2004)
Birth-death processes with disaster and instantaneous resurrection.
*Advances in Applied Probability* 36, 267-292.
[MR 2004k:60204]

Chen, A., Pollett, P.K., Zhang, H. and Li, J. (2004)
The collision branching process.
*Journal of Applied Probability* 41, 1033-1048.
[MR 2006m:60124]

Chen, A., Pollett, P.K., Zhang, H. and Cairns, B. (2005)
Uniqueness criteria for continuous-time Markov chains
with general transition structures.
*Advances in Applied Probability* 37, 1056-1074.
[MR 2006k:60138]

Clancy, D., O'Neill, P.D. and Pollett, P.K. (2001)
Approximations for the long-term behaviour of an open-population
epidemic model.
*Methodology and Computing in Applied Probability* 3, 75-95.
[MR 2002c:92031]

Clancy, D. and Pollett, P.K. (2003)
A note on quasi-stationary distributions of birth-death processes
and the SIS logistic epidemic.
*Journal of Applied Probability* 40, 821-825.
[MR 2004d:60198]

Dong, Y. and Zhang, H. (2003)
Ruin probability in risk model with two Poisson processes by diffusion.
*Mathematical Theory and Applications* 23, 98-101.
[MR1994850]

Gray, B., Pollett, P.K. and Zhang, H. (2005)
On the existence of uni-instantaneous *Q*-processes with a
given finite m-invariant measure.
*Journal of Applied Probability* 42, 713-725.
[MR 2006d:60119]

Liu, K. and Chen, A. (2001)
Moment decay rates of solutions of stochastic differential equations.
*The Tohoku Mathematical Journal* 53, 81-93.
[MR 2001k:60080]

Liu, K. and Chen, A. (2001)
A class of generalized Lévy Laplacians in infinite dimensional
calculus.
*Israel Journal of Mathematics* 124, 157-176.
[MR 2002h:46064]

Lin, X., Zhang, H. and Hou, Z. (2002)
The m-invariant distribution of a *Q*-process.
*Acta Mathematicae Applicatae Sinica* 25, 694-703.
[MR 2004f:60154]

Lin, X., Zhang, H. and Hou, Z. (2003)
Invariant distribution for jump processes.
*Advances in Mathematics (China)* 32, 466-472.
[MR 2004f:60179]

Lu, W., Yuan, C. and Zhang, H. (2002)
Heavy traffic limit theorems for Lu-Kumar reentrant queueing networks.
*Mathematics in Economics* 19, 55-59.
[MR 2004f:60154]

Pollett, P.K. (2001)
Quasistationarity in populations that are subject to large-scale
mortality or emigration.
*Environment International* 27, 231-236.

Pollett, P.K. (2001)
Similar Markov chains.
*Journal of Applied Probability* 38A, 53-65.
[MR 2003e:60171]

Pollett, P.K. (2002)
Identifying *Q*-processes with a given finite
m-invariant measure.
In (Eds Zhenting Hou, Jerzy A. Filar and Anyue Chen)
* Markov Processes and Controlled Markov Chains*, Kluwer, pp. 41-55.
[MR 2004k:60210]

Pollett, P.K. and Stefanov, V.T. (2002)
Path integrals for continuous-time Markov chains.
*Journal of Applied Probability* 39,
901-904.
[MR 2003i:60124]

Pollett, P.K. (2003)
Integrals for continuous-time Markov chains.
*Mathematical Biosciences* 182, 113-225.
[MR 2004c:60213]

Pollett, P.K. and Thompson, M.R. (2003)
A new method for analysing the equilibrium and time-dependent behaviour
of Markovian models.
*Mathematical and Computer Modelling* 38, 1409-1418.
[MR2028324]

Pollett, P.K. and Zhang, H. (2004)
Existence and uniqueness of *Q*-processes with a given
finite m-invariant measure.
In (Eds. Philip K. Pollett and Peter G. Taylor)
*Festschrift in Honour of Daryl Daley*,
*Australian & New Zealand Journal of Statistics* 46,
113-120.
[MR 2005h:60232]

Wu, Q. and Zhang, H. (2003) An extended birth-death process.
*Journal of Systems Science and Mathematical Sciences* 23, 517-528.
[MR 2004k:60234]

Wu, Q., Zhang, H. and Hou, Z. (2003)
An extended birth-death *Q*-matrix with instantaneous state
and catastrophes I.
*Chinese Annals of Mathematics, Series A* 24, 187-192.
(English translation in
*Chinese Journal of Contemporary Mathematics* 24, 159-168.)
[MR 2004h:60133]

Wu, Q., Zhang, H. and Hou, Z. (2003)
An extended birth-death *Q*-matrix with instantaneous state
and catastrophes II.
*Chinese Annals of Mathematics, Series A* 24, 555-564.
(English translation in
*Chinese Journal of Contemporary Mathematics* 24, 317-328.)
[MR 2005f:60161]

Zeng, A., Lin, X. and Zhang, H. (2003)
A Cox risk model of double line.
*Mathematical Theory and Applications (Changsha)* 23,
107-112.
[MR1994852]

Zhang, H., Chen, A., Lin, X. and Hou, Z. (2001)
Strong ergodicity of monotone transition functions.
*Statistics & Probability Letters* 55, 63-69.
[MR 2002g:60115]

Zhang, H., Lin, X. and Hou, Z. (2001)
Invariant distributions of *Q*-processes I.
*Chinese Annals of Mathematics, Series A* 22, 323-330.
[MR 2002h:60157]

Zhang, H., Lin, X. and Hou, Z. (2002)
Invariant distributions of *Q*-processes II.
*Chinese Annals of Mathematics, Series A* 23, 361-370.
[MR 2003i:60126]

Zhang, H., Mei, Q., Lin, X. and Hou, Z. (2002)
Convergence property of standard transition functions.
In (Eds Zhenting Hou, Jerzy A. Filar and Anyue Chen)
* Markov Processes and Controlled Markov Chains*, Kluwer, pp. 57-67.
[MR 2005b:60201]

Papers in refereed conference proceedings (E1)

Cairns, B.J. and Pollett, P.K. (2003)
Evaluating persistence times in populations that are subject
to local catastrophes.
In (Ed. David A. Post)
* Proceedings of the International Congress on Modelling
and Simulation*, Vol 2 (ISBN 1-74052-098-X)
Modelling and Simulation Society of Australia and New Zealand,
Townsville, Australia, pp. 747-752.

Pollett, P.K. (2001)
Diffusion approximations for ecological models.
In
(Ed. Fred Ghassemi)
* Proceedings of the International Congress on Modelling
and Simulation*, Vol.2,
Modelling and Simulation Society of Australia and New Zealand,
Canberra, Australia, pp. 843-848.

Pollett, P.K. and Stefanov, V.T. (2003)
A method for evaluating the distribution of the total cost of a
random process over its lifetime.
In (Ed. David A. Post)
* Proceedings of the International Congress on Modelling
and Simulation*, Vol 4, (ISBN 1-74052-098-X)
Modelling and Simulation Society of Australia and New Zealand,
Townsville, Australia, pp. 1863-1867.

Edited volumes (C5)

Hou, Z., Filar, J.A. and Chen, A. (2002)
* Markov Processes and Controlled Markov Chains*.
Papers
from the International Workshop held in Changsha, August 22-28, 1999.
Kluwer Academic
Publishers, Dordrecht, x+511 pp. ISBN: 1-4020-0803-1 60-06
[MR 2004f:60003]

Pollett, P.K. and Taylor, P.G. (2004)
Festschrift in Honour of Daryl Daley,
*Australian & New Zealand Journal of Zealand Journal of
Statistics* 46 (1).
Print ISSN: 1369-1473,
Online ISSN: 1467-842X.
[MR2055792]

Technical reports

Pollett, P.K. and Stefanov, V.T. (2002)
Path integrals for continuous-time Markov chains.
* Technical Report*, Discipline of Mathematics,
The University of Queensland.

Invited conference presentations (E4)

Pollett, P.K. Similar Markov Chains, Symposium in Honour of David Vere-Jones on the Occasion of his 65th Birthday, Victoria University of Wellington, Wellington, New Zealand, April 19-21, 2001.

Pollett, P.K. Pakes' Contribution to Markov Chain Theory, Workshop in honour of Tony Pakes on the occasion of his 60th birthday, Department of Mathematics and Statistics, University of Western Australia, Perth, Australia, 2 October, 2001.

Pollett, P.K. Identifying Markov chains with a given invariant measure, The Oberwolfach Applied Probability Meeting, Mathematisches Forschungsinstitut Oberwolfach, Germany, 30 November-6 December, 2003.

Contributed conference presentations (E4)

Cairns, B.J. and Pollett, P.K. Evaluating persistence times in populations that are subject to local catastrophes, International Congress on Modelling and Simulation (MODSIM 2003), Townsville, Queensland, Australia, 14-17 July, 2003.

Pollett, P.K.
Identifying *Q*-processes with a given finite m-invariant
measure,
27th Conference on Stochastic Processes and their Applications,
Centre for Mathematical Sciences, Cambridge, UK, 9-13 July, 2001.

Pollett, P.K. and Stefanov, V.T. A method for evaluating the distribution of the total cost of a random process over its lifetime, International Congress on Modelling and Simulation (MODSIM 2003), Townsville, Queensland, Australia, 14-17 July, 2003.

If you have any comments on these pages,

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