Institute of Mathematics and Statistics
University of Kent
Canterbury, CT2 7NF, UK
office hours (S05) for the autumn term 2014: Wednesday 11.00 - 12.00 and Thursday 10.00 - 11.00
e-mail: L.Breuer@kent.ac.uk
Course Material on Stochastic Processes:
Selected Publications
Queueing theory
The Periodic BMAP/PH/c Queue, Queueing Systems 38 (2001), pp.67-76.
A Retrial BMAP/PH/N System, Queueing Systems 40 (2002), pp.431--455.
"From Markov jump processes to spatial queues", Springer, 2003
Transient and Stationary Distributions for the GI/G/k Queue with Lebesgue-Dominated Inter-Arrival Time Distribution, Queueing Systems 45 (2003), pp.47-57
"An Introduction to Queueing Theory and Matrix-Analytic Methods", Springer, 2005
"Applying Foster´s criteria to a GI/PH/1 queueing system", Cybernetics and Systems Analysis 42(3), pp.433-439, 2006
"Continuity of the M/G/c queue", Queueing Systems 58:321-331, 2008
The Total Overflow during a Busy Cycle in a Markov-Additive Finite Buffer System, B. Muller-Clostermann, K. Echtle, E. Rathgeb (Eds.): MMB & DFT 2010, LNCS 5987, pp. 198--211. Springer, Heidelberg (2010)
Statistics
An EM algorithm for Batch Markovian Arrival Processes and its comparison to a simpler estimation procedure, Annals of Operations Research 112 (2002), pp.123--138
"An EM algorithm for platoon arrival processes in discrete time", Operations Research Letters 33, pp.535-543, 2005
An EM algorithm for Markovian arrival processes observed at discrete times, B. Muller-Clostermann, K. Echtle, E. Rathgeb (Eds.): MMB & DFT 2010, LNCS 5987, pp. 242--258. Springer, Heidelberg (2010)
Risk theory and fluid flows
"Risk processes analyzed as fluid queues", Scandinavian Actuarial Journal 2005(2), pp.127-141
"Phase-type approximations to finite-time ruin probabilities in the Sparre Andersen and stationary renewal risk models", ASTIN Bulletin 35(1), pp.131-144, 2005
"The surplus prior to ruin and the deficit at ruin for a correlated risk process", Scandinavian Actuarial Journal 2005(6), pp.433-445
"The use of vector-valued martingales in risk theory", Blatter der DGVFM 29(1):1-12, 2008
"Threshold dividend strategies for a Markov-additive risk model", European Actuarial Journal 1(2):237-258
"A generalised Gerber-Shiu measure for Markov-additive risk processes with phase-type claims and capital injections", Scandinavian Actuarial Journal, to appear
Markov-additive processes
"First passage times for Markov-additive processes with positive jumps of phase-type", J. Appl. Prob. 45(3):779-799, 2008
"A quintuple law for Markov-additive processes with phase-type jumps", J. Appl. Prob. 47(2):441-458, 2010
"Exit problems for reflected Markov-modulated Brownian motion", J. Appl. Prob. 49(3):697-709, 2012
"Occupation times for Markov-modulated Brownian motion", J. Appl. Prob. 49(2):549-565, 2012
"The resolvent and expected local times for Markov-modulated Brownian motion with phase dependent termination rates", J. Appl. Prob. 50(2):430-438, 2013
Miscellaneous
On Markov-Additive Jump Processes, Queueing Systems 40 (2002), pp.75--91.
A piecewise-deterministic Model for Brownian Motion, Theory of Stochastic Processes 8(24), N1-2, pp.40-46
"Approximating diffusions by piecewise constant parameters", submitted