# Author Publications

**78**.

## 2016

Doorn, Erik A. van
(2016)
*Shell polynomials and dual birth-death processes.*
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 12
.
049.
ISSN 1815-0659

## 2015

Doorn, E.A. van
(2015)
*Shell polynomials and dual birth-death processes.*
[Report]

Doorn, Erik A. van
(2015)
*Spectral properties of birth-death polynomials.*
Journal of computational and applied mathematics, 284
.
pp. 251-258.
ISSN 0377-0427

Doorn, Erik A. van
(2015)
*Representations for the decay parameter of a birth-death process based on the Courant-Fischer theorem.*
Journal of applied probability, 52
(1).
pp. 278-289.
ISSN 0021-9002

Doorn, Erik A. van
(2015)
*An orthogonal-polynomial approach to first-hitting times of birth-death processes.*
[Report]

## 2014

Doorn, Erik A. van
(2014)
*Representations for the decay parameter of a birth-death process based on the Courant-Fischer Theorem.*
[Report]

Doorn, Erik A. van
(2014)
*Spectral properties of birth-death polynomials.*
[Report]

## 2013

Doorn, Erik A. van
(2013)
*Weighted sums of orthogonal polynomials related to birth-death processes with killing.*
Advances in dynamical systems and applications, 8
(2).
pp. 401-412.
ISSN 0973-5321

Doorn, Erik A. van and Foreest, Nicky van and Zeifman, Alexander I.
(2013)
*Corrigendum to “Representations for the extreme zeros of orthogonal polynomials” [J. Comput. Appl. Math. 233 (2009) 847–851].*
Journal of Computational and Applied Mathematics, 244
.
pp. 155-156.
ISSN 0377-0427

Doorn, Erik A. van and Pollett, Philip K.
(2013)
*Quasi-stationary distributions for discrete-state models.*
European journal of operational research, 230
(1).
pp. 1-14.
ISSN 0377-2217

## 2012

Doorn, Erik A. van
(2012)
*Conditions for the existence of quasi-stationary distributions for birth-death processes with killing.*
Stochastic Processes and Their Applications, 122
(6).
pp. 2400-2410.
ISSN 0304-4149

Doorn, Erik A. van
(2012)
*Weighted sums of orthogonal polynomials related to birth-death processes with killing.*
[Report]

## 2011

Doorn, Erik A. van
(2011)
*Conditions for the existence of quasi-stationary distributions for birth-death processes with killing.*
[Report]

Doorn, Erik A. van
(2011)
*Rate of convergence to stationarity of the system .*
TOP, 19
(2).
pp. 336-350.
ISSN 1134-5764

Doorn, Erik A. van and Pollett, Philip K.
(2011)
*Quasi-stationary distributions.*
[Report]

## 2010

Doorn, E.A. van
(2010)
*Rate of convergence to stationarity of the system .*
[Report]

Doorn, E.A. van and Zeifman, A.I. and Panfilova, T.L.
(2010)
*Bounds and asymptotics for the rate of convergence of birth-death processes.*
Theory of Probability and its Applications, 54
(1).
pp. 97-113.
ISSN 0040-585X

## 2009

Doorn, E.A. van and Zeifman, A.I. and Panfilova, T.L.
(2009)
*Bounds and asymptotics for the rate of convergence of birth-death processes.*
Teoriya Veroyatnostei i ee Primeneniya, 54
(1).
pp. 18-38.
ISSN 0040-361X

Doorn, Erik A. van and Foreest, Nicky D. van and Zeifman, Alexander I.
(2009)
*Representations for the extreme zeros of orthogonal polynomials.*
Journal of Computational and Applied Mathematics, 233
(3).
pp. 847-851.
ISSN 0377-0427

Doorn, Erik A. van and Zeifman, Alexander I.
(2009)
*On the speed of convergence to stationarity of the Erlang loss system.*
[Report]

Doorn, Erik A. van and Zeifman, Alexander I.
(2009)
*On the speed of convergence to stationarity of the Erlang loss system.*
Queueing Systems, 63
(1-4).
pp. 241-252.
ISSN 0257-0130

Pollett, P.K. and Doorn, E.A. van
(2009)
*Quasi-stationary distributions for reducible absorbing Markov chains in discrete time.*
Markov Processes and Related Fields, 15
(2).
pp. 191-204.
ISSN 1024-2953

## 2008

Doorn, Erik A. van and Pollett, Philip K.
(2008)
*Survival in a quasi-death process.*
Linear Algebra and its Applications, 429
(4).
pp. 776-791.
ISSN 0024-3795

Doorn, Erik A. van and Zeifman, Alexander I. and Panfilova, Tatyana L.
(2008)
*Bounds and asymptotics for the rate of convergence of birth-death processes.*
[Report]

Pollett, P.K. and Doorn, E.A. van
(2008)
*Quasi-stationary distributions for reducible absorbing Markov chains in discrete time.*
[Report]

## 2007

Coolen-Schrijner, Pauline and Doorn, Erik A. van
(2007)
*Orthogonal polynomials on and birth-death processes with killing.*
In: International Conference on Difference Equations, Special Functions and Orthogonal Polynomials, 25-30 July 2005, Munich, Germany (pp. pp. 726-740).

Doorn, Erik A. van and Foreest, Nicky D. van and Zeifman, Alexander I.
(2007)
*Representations for the extreme zeros of orthogonal polynomials.*
[Report]

Doorn, Erik A. van and Pollett, Philip K.
(2007)
*Survival in a quasi-death process.*
[Report]

## 2006

Coolen-Schrijner, Pauline and Doorn, Erik A. van
(2006)
*Quasi-stationary distributions for a class of discrete-time Markov chains.*
Methodology and Computing in Applied Probability, 8
(4).
pp. 449-465.
ISSN 1387-5841

Coolen-Schrijner, Pauline and Doorn, Erik A. van
(2006)
*Quasi-stationary distributions for birth-death processes with killing.*
Journal of Applied Mathematics and Stochastic Analysis, 2006
.
p. 84640.
ISSN 1048-9533

Doorn, Erik A. van
(2006)
*On the α-classification of birth-death and quasi-birth-death processes.*
Stochastic Models, 22
(3).
pp. 411-421.
ISSN 1532-6349

## 2005

Coolen-Schrijner, P. and Doorn, E.A. van
(2005)
*Birth-death processes with killing: orthogonal polynomials and quasi-stationary distributions.*
[Report]

Coolen-Schrijner, P. and Doorn, E.A. van
(2005)
*Orthogonal polynomials on and birth-death processes with killing.*
[Report]

Doorn, E.A. van
(2005)
*On the -classification of birth-death and quasi-birth-death processes.*
[Report]

Doorn, Erik A. van and Zeifman, Alexander I.
(2005)
*Birth-death processes with killing.*
Statistics & Probability Letters, 72
(1).
pp. 33-42.
ISSN 0167-7152

Doorn, Erik A. van and Zeifman, Alexander I.
(2005)
*Extinction probability in a birth-death process with killing.*
Journal of Applied Probability, 42
(1).
pp. 185-198.
ISSN 0021-9002

## 2004

Coolen-Schrijner, P. and Doorn, E.A. van
(2004)
*Quasi-stationary distributions for a class of discrete-time Markov chains.*
[Report]

Doorn, E.A. van and Jagers, A.A.
(2004)
*A note on the system with identical service and interarrival-time distributions.*
Queueing Systems, 47
(1-2).
pp. 45-52.
ISSN 0257-0130

Doorn, E.A. van and Zeifman, A.I.
(2004)
*Birth-death processes with killing.*
[Report]

Doorn, E.A. van and Zeifman, A.I.
(2004)
*Extinction probability in a birth-death process with killing.*
[Report]

## 2003

Doorn, Erik A. van
(2003)
*Birth-death processes and associated polynomials.*
Journal of Computational and Applied Mathematics, 153
(1-2).
pp. 497-506.
ISSN 0377-0427

Doorn, Erik A. van
(2003)
*On associated polynomials and decay rates for birth-death processes.*
Journal of Mathematical Analysis and Applications, 278
(2).
pp. 500-511.
ISSN 0022-247X

Doorn, Erik A. van and Ta, An T.K.
(2003)
*Proofs for some conjectures of Rajaratnam and Takawira on the peakedness of handoff traffic.*
IEEE Transactions on Vehicular Technology, 52
(4).
pp. 953-957.
ISSN 0018-9545

## 2002

Coolen-Schrijner, Pauline and Doorn, Erik A. van
(2002)
*The deviation matrix of a continuous-time Markov chain.*
Probability in the Engineering and Informational Sciences, 16
(3).
pp. 351-366.
ISSN 0269-9648

Doorn, E.A. van and Jagers, A.A.
(2002)
*A note on the system with identical service and interarrival-time distributions.*
[Report]

Doorn, E.A. van and Kieu, A.T.T.
(2002)
*Proofs for some conjectures of Rajaratnam and Takawira.*
[Report]

Doorn, Erik A. van
(2002)
*Representations for the rate of convergence of birth-death processes.*
Theory of Probability and Mathematical Statistics, 65
.
pp. 37-43.
ISSN 1547-7363

Malhotra, R. and Dey, D. and Doorn, E.A. van and Koonen, A.M.J.
(2002)
*Traffic modelling in a reconfigurable broadband nomadic computing environment.*
Performance Evaluation, 47
(4).
pp. 255-267.
ISSN 0166-5316

## 2001

Coolen-Schrijner, P. and Doorn, E.A. van
(2001)
*The deviation matrix of a continuous-time Markov chain.*
[Report]

Coolen-Schrijner, Pauline and Doorn, Erik A. van
(2001)
*On the convergence to stationarity of birth-death processes.*
Journal of Applied Probability, 38
(3).
pp. 696-706.
ISSN 0021-9002

Doorn, E.A. van
(2001)
*Associated polynomials and birth-death processes.*
[Report]

Doorn, E.A. van
(2001)
*Representations for the rate of convergence of birth-death processes.*
[Report]

Doorn, E.A. van
(2001)
*On associated polynomials and decay rates for birth-death processes.*
[Report]

## 2000

Coolen-Schrijner, P. and Doorn, E.A. van
(2000)
*On the convergence to stationarity of birth-death processes.*
[Report]

Lenin, R.B. and Parthasarathy, P.R. and Scheinhardt, W.R.W. and Doorn, E.A. van
(2000)
*Families of birth-death processes with similar time-dependent behaviour.*
Journal of Applied Probability, 37
(3).
pp. 835-849.
ISSN 0021-9002

## 1999

Lenin, R.B. and Parthasarathy, P.R. and Scheinhardt, W.R.W. and Doorn, E.A. van
(1999)
*Families of birth-death processes with similar time-dependent behaviour.*
[Report]

## 1998

Adan, I.J.B.F. and Doorn, E.A. van and Resing, J.A.C. and Scheinhardt, W.R.W.
(1998)
*Analysis of a single server queue interacting with a fluid reservoir.*
Queueing Systems, 29
(2-4).
pp. 313-336.
ISSN 0257-0130

Boucherie, Richard J. and Doorn, Erik A. van
(1998)
*Uniformization for λ-positive Markov chains.*
Stochastic Models, 14
(1 & 2).
pp. 171-186.
ISSN 1532-6349

Coolen-Schrijner, Pauline and Doorn, Erik A. van
(1998)
*Analysis of random walks using orthogonal polynomials.*
Journal of Computational and Applied Mathematics, 99
(1-2).
pp. 387-399.
ISSN 0377-0427

## 1997

Chen, C.H. and Bouwmeester, H.J.M. and Doorn, E.A. van and Kruidhof, H. and Burggraaf, A.J.
(1997)
*Oxygen permeation of La0.3Sr0.7CoO3-d.*
Solid State Ionics, 98
(1-2).
pp. 7-13.
ISSN 0167-2738

Coolen-Schrijner, Pauline and Doorn, Erik A. van
(1997)
*Weak convergence of conditioned birth-death processes in discrete time.*
Journal of Applied Probability, 34
(1).
pp. 46-53.
ISSN 0021-9002

Kijima, M. and Nair, M.G. and Pollett, P.K. and Doorn, E.A. van
(1997)
*Limiting conditional distributions for birth-death processes.*
Advances in Applied Probability, 29
(1).
pp. 185-204.
ISSN 0001-8678

## 1996

Adan, I.J.B.F. and Doorn, E.A. van and Resing, J.A.C. and Scheinhardt, W.R.W.
(1996)
*A queueing system with two different service speeds.*
[Report]

Doorn, E.A. van and Scheinhardt, W.R.W.
(1996)
*Analysis of birth-death fluid queues.*
[Report]

## 1995

Doorn, Erik A. van
(1995)
*Some new results for chain-sequence polynomials.*
Journal of Computational and Applied Mathematics, 57
(1-2).
pp. 309-317.
ISSN 0377-0427

Doorn, Erik A. van and Schrijner, Pauline
(1995)
*Ratio limits and limiting conditional distributions for discrete-time birth-death processes.*
Journal of Mathematical Analysis and Applications, 190
(1).
pp. 263-284.
ISSN 0022-247X

Kijima, Masaaki and Doorn, Erik A. van
(1995)
*Weighted sums of orthogonal polynomials with positive zeros.*
Journal of Computational and Applied Mathematics, 65
(1-3).
pp. 195-206.
ISSN 0377-0427

## 1993

Doorn, Erik A. van and Panken, Frans J.M.
(1993)
*Blocking probabilities in a loss system with arrivals in geometrically distributed batches and heterogeneous service requirements.*
IEEE/ACM transactions on networking, 1
(6).
pp. 664-667.
ISSN 1063-6692

Doorn, Erik A. van and Schrijner, Pauline
(1993)
*Random walk polynomials and random walk measures.*
Journal of Computational and Applied Mathematics, 49
(1-3).
pp. 289-296.
ISSN 0377-0427

## 1990

Arem, Bart van and Doorn, Erik A. van
(1990)
*Analysis of a queuing model for slotted ring networks.*
Computer networks and ISDN systems, 20
(1-5).
pp. 309-314.
ISSN 0169-7552

## 1988

Doorn, Erik A. van and Regterschot, G.J.K.
(1988)
*Conditional PASTA.*
Operations research letters, 71
(5).
pp. 229-232.
ISSN 0167-6377

Mehta, Madan Lal and Doorn, Erik A. van
(1988)
*Inequalities for Charlier polynomials with application to teletraffic theory.*
Journal of Mathematical Analysis and Applications, 133
(2).
pp. 449-460.
ISSN 0022-247X

## 1987

Doorn, Erik A. van
(1987)
*Representations and bounds for zeros of orthogonal polynomials and eigenvalues of sign-symmetric tri-diagonal matrices.*
Journal of Approximation Theory, 51
(3).
pp. 254-266.
ISSN 0021-9045

Doorn, Erik A. van
(1987)
*The indeterminate rate problem for birth-death processes.*
Pacific Journal of Mathematics, 130
(2).
pp. 379-393.
ISSN 0030-8730

## 1986

Doorn, Erik A. van
(1986)
*A note on orthogonal polynomials and oscillation criteria for second order linear difference equations.*
Journal of Mathematical Analysis and Applications, 120
(1).
pp. 354-359.
ISSN 0022-247X

Doorn, Erik A. van
(1986)
*Connectivity of circulant digraphs.*
Journal of Graph Theory, 10
(1-4).
pp. 9-14.
ISSN 0364-9024

Jagers, A.A. and Doorn, Erik A. van
(1986)
*On the continued Erlang loss function.*
Operations Research Letters, 5
(1).
pp. 43-46.
ISSN 0167-6377

## 1981

Doorn, Erik A. van
(1981)
*On the time dependent behaviour of the truncated birth-death process.*
Stochastic Processes and Their Applications, 11
(3).
pp. 261-271.
ISSN 0304-4149

**Sun Jul 24 05:29:29 2016 CEST**.