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Erik Alexander van Doorn

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1981 …2019
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Research Output 1981 2019

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Article
2019

On a property of random walk polynomials involving Christoffel functions

van Doorn, E. A. & Szwarc, R., 1 Sep 2019, In : Journal of mathematical analysis and applications. 477, 1, p. 85-103 19 p.

Research output: Contribution to journalArticleAcademicpeer-review

Random walk
Polynomials
Polynomial
Birth-death Process
Equivalence
2018
5 Downloads (Pure)

Asymptotic period of an aperiodic Markov chain

van Doorn, E. A., 2018, In : Markov processes and related fields. 24, 5, p. 759-778 20 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Markov processes
Markov chain
Birth-death Process
Transition Probability
Countable
2 Citations (Scopus)
35 Downloads (Pure)

On the strong ratio limit property for discrete-time birth-death processes

van Doorn, E. A., 15 May 2018, In : Symmetry, integrability and geometry : methods and applications (SIGMA). 14, 9 p., 047.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Birth-death Process
Discrete-time
Sufficient Conditions
Transition Probability
2017
49 Downloads (Pure)

An orthogonal-polynomial approach to first-hitting times of birth-death processes

van Doorn, E. A., Jun 2017, In : Journal of Theoretical Probability. 30, 2, p. 594-607 13 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
First Hitting Time
Birth-death Process
Orthogonal Polynomials
Associated Polynomials
Dirichlet Form
2016
38 Downloads (Pure)

Shell polynomials and dual birth-death processes

van Doorn, E. A., 18 May 2016, In : Symmetry, integrability and geometry : methods and applications (SIGMA). 12, p. 049 15 p.

Research output: Contribution to journalArticleAcademicpeer-review

File
2015
5 Citations (Scopus)

Representations for the decay parameter of a birth-death process based on the Courant-Fischer theorem

van Doorn, E. A., 2015, In : Journal of applied probability. 52, 1, p. 278-289 12 p.

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)

Spectral properties of birth-death polynomials

van Doorn, E. A., 15 Aug 2015, In : Journal of computational and applied mathematics. 284, p. 251-258 8 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Spectral Properties
Polynomials
Three-term Recurrence Relations
Birth-death Process
Polynomial
2013
18 Downloads (Pure)

Corrigendum to “Representations for the extreme zeros of orthogonal polynomials” [J. Comput. Appl. Math. 233 (2009) 847–851]

van Doorn, E. A., van Foreest, N. D. & Zeifman, A. I., 2013, In : Journal of computational and applied mathematics. 244, p. 155-156

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Applied mathematics
Orthogonality
Orthogonal Polynomials
Extremes
Polynomials
29 Citations (Scopus)
41 Downloads (Pure)

Quasi-stationary distributions for discrete-state models

van Doorn, E. A. & Pollett, P. K., 2013, In : European journal of operational research. 230, 1, p. 1-14 14 p.

Research output: Contribution to journalArticleAcademicpeer-review

File
13 Downloads (Pure)

Weighted sums of orthogonal polynomials related to birth-death processes with killing

van Doorn, E. A., 2013, In : Advances in dynamical systems and applications. 8, 2, p. 401-412 12 p.

Research output: Contribution to journalArticleAcademicpeer-review

File
2012
5 Citations (Scopus)

Conditions for the existence of quasi-stationary distributions for birth-death processes with killing

van Doorn, E. A., 2012, In : Stochastic processes and their applications. 122, 6, p. 2400-2410 11 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Quasi-stationary Distribution
Birth-death Process
Decay Rate
Absorbing
Exceed
2011
1 Citation (Scopus)

Rate of convergence to stationarity of the system $M/M/N/N+R$

van Doorn, E. A., Dec 2011, In : Top. 19, 2, p. 336-350 15 p.

Research output: Contribution to journalArticleAcademicpeer-review

2010
25 Citations (Scopus)
43 Downloads (Pure)

Bounds and asymptotics for the rate of convergence of birth-death processes

van Doorn, E. A., Zeifman, A. I. & Panfilova, T. L., 2010, In : Theory of probability and its applications. 54, 1, p. 97-113 22 p., 10.1137/S0040585X97984097.

Research output: Contribution to journalArticleAcademicpeer-review

File
2009

Bounds and asymptotics for the rate of convergence of birth-death processes

van Doorn, E. A., Zeifman, A. I. & Panfilova, T. L., 2009, In : Teoriya veroyatnostei i ee primeneniya. 54, 1, p. 18-38 22 p.

Research output: Contribution to journalArticleAcademicpeer-review

27 Downloads (Pure)

On the speed of convergence to stationarity of the Erlang loss system

van Doorn, E. A. & Zeifman, A. I., Jul 2009, In : Queueing systems. 63, 1-4, p. 241-252 12 p., 10.1007/s11134-009-9134-9.

Research output: Contribution to journalArticleAcademicpeer-review

File

Quasi-stationary distributions for reducible absorbing Markov chains in discrete time

van Doorn, E. A. & Pollett, P. K., 2009, In : Markov processes and related fields. 15, 2, p. 191-204 16 p.

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)
30 Downloads (Pure)

Representations for the extreme zeros of orthogonal polynomials

van Doorn, E. A., van Foreest, N. D. & Zeifman, A. I., 2009, In : Journal of computational and applied mathematics. 233, 3, p. 847-851 5 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Orthogonal Polynomials
Extremes
Polynomials
Three-term Recurrence Relations
Birth-death Process
2008
19 Citations (Scopus)
24 Downloads (Pure)

Survival in a quasi-death process

van Doorn, E. A. & Pollett, P. K., 2008, In : Linear algebra and its applications. 429, 4, p. 776-791 14 p., 10.1016/j.laa.2008.04.004.

Research output: Contribution to journalArticleAcademicpeer-review

File
2006
5 Citations (Scopus)
37 Downloads (Pure)

On the α-classification of birth-death and quasi-birth-death processes

van Doorn, E. A., 2006, In : Stochastic models. 22, 2, p. 411-421 11 p., 10.1080/15326340600820364.

Research output: Contribution to journalArticleAcademicpeer-review

File
13 Citations (Scopus)

Quasi-stationary distributions for a class of discrete-time Markov chains

Coolen-Schrijner, P. & van Doorn, E. A., 1 Dec 2006, In : Methodology and computing in applied probability. 8, 4, p. 449-465 17 p.

Research output: Contribution to journalArticleAcademicpeer-review

Quasi-stationary Distribution
Markov chain
Discrete-time
Absorption
Absorbing
7 Citations (Scopus)
5 Downloads (Pure)

Quasi-stationary distributions for birth-death processes with killing

Coolen-Schrijner, P. & van Doorn, E. A., 2006, In : Journal of applied mathematics and stochastic analysis. 2006, 2, 15 p., 84640.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Quasi-stationary Distribution
Birth-death Process
Absorbing
Polynomials
Stationarity
2005
17 Citations (Scopus)
51 Downloads (Pure)

Birth-death processes with killing

van Doorn, E. A. & Zeifman, A. I., 2005, In : Statistics & probability letters. 72, 1, p. 33-42 10 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Birth-death Process
Transition Probability
Absorbing
Integral Representation
Absorption
21 Citations (Scopus)
293 Downloads (Pure)

Extinction probability in a birth-death process with killing

van Doorn, E. A. & Zeifman, A. I., 2005, In : Journal of applied probability. 42, 1, p. 185-198 14 p.

Research output: Contribution to journalArticleAcademicpeer-review

File
2004
3 Citations (Scopus)

A Note on the GI/GI/∞ System with Identical Service and Interarrival-Time Distributions

van Doorn, E. A. & Jagers, A. A., 2004, In : Queueing systems. 47, 1-2, p. 45-52 7 p.

Research output: Contribution to journalArticleAcademicpeer-review

Servers
Gamma distribution
Stationary Distribution
Server
Verify
2003
12 Citations (Scopus)

Birth-death processes and associated polynomials

van Doorn, E. A., 2003, In : Journal of computational and applied mathematics. 153, 1-2, p. 497-506 10 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Birth-death Process
Birth and Death Process
Associated Polynomials
Polynomials
Recurrence
8 Citations (Scopus)
23 Downloads (Pure)

On associated polynomials and decay rates for birth-death processes

van Doorn, E. A., 2003, In : Journal of mathematical analysis and applications. 278, 2, p. 500-511 11 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Birth-death Process
Associated Polynomials
Decay Rate
Polynomials
Orthogonal Polynomials
3 Citations (Scopus)

Proofs for some conjectures of Rajaratnam and Takawira on the peakedness of handoff traffic

van Doorn, E. A. & Ta, A. T. K., 2003, In : IEEE transactions on vehicular technology. 52, 4, p. 953-957

Research output: Contribution to journalArticleAcademicpeer-review

Peakedness
Handoff
Performance Analysis
Traffic
System of Nonlinear Equations
2002

Representations for the rate of convergence of birth-death processes

van Doorn, E. A., 2002, In : Theory of probability and mathematical statistics. 65, p. 37-43 8 p.

Research output: Contribution to journalArticleAcademicpeer-review

42 Citations (Scopus)

The deviation matrix of a continuous-time Markov chain

Coolen-Schrijner, P. & van Doorn, E. A., 2002, In : Probability in the engineering and informational sciences. 16, 3, p. 351-366 15 p.

Research output: Contribution to journalArticleAcademicpeer-review

Continuous-time Markov Chain
Markov processes
Deviation
Pi
Birth-death Process

Traffic modeling in a reconfigurable broadband nomadic computing environment

Malhotra, R., van Doorn, E. A., Dey, D. & Koonen, A. M. J., 2002, In : Performance evaluation. 47, p. 255-267

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)

Traffic modelling in a reconfigurable broadband nomadic computing environment

Malhotra, R., Dey, D., van Doorn, E. A. & Koonen, A. M. J., 2002, In : Performance evaluation. 47, 4, p. 255-267 10 p., 10.1016/S0166-5316(01)00067-0.

Research output: Contribution to journalArticleAcademicpeer-review

2001

On the convergence to stationarity of birth-death processes

van Doorn, E. A., 2001, In : Journal of applied probability. 38, p. 696-706

Research output: Contribution to journalArticleAcademicpeer-review

12 Citations (Scopus)

On the convergence to stationarity of birth-death processes

Coolen-Schrijner, P. & van Doorn, E. A., 2001, In : Journal of applied probability. 38, 3, p. 696-706 10 p., 10.1239/jap/1005091033.

Research output: Contribution to journalArticleAcademicpeer-review

2000
16 Citations (Scopus)

Families of birth-death processes with similar time-dependent behaviour.

Lenin, R. B., Parthasarathy, P. R., Scheinhardt, W. R. W. & van Doorn, E. A., 2000, In : Journal of applied probability. 2000, 37, p. 835-849 14 p., 10.1239/jap/1014842840.

Research output: Contribution to journalArticleAcademicpeer-review

1998
17 Citations (Scopus)

Analysis of a single server queue interacting with a fluid reservoir

Adan, I. J. B. F., van Doorn, E. A., Resing, J. A. C. & Scheinhardt, W. R. W., 1998, In : Queueing systems. 29, 2-4, p. 313-336 22 p.

Research output: Contribution to journalArticleAcademicpeer-review

3 Downloads (Pure)

Analysis of random walks using orthogonal polynomials

Coolen-Schrijner, P. & van Doorn, E. A., 1998, In : Journal of computational and applied mathematics. 99, 99, p. 387-399 13 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Birth-death Process
Orthogonal Polynomials
Random walk
Discrete-time
Polynomials

Uniformization for λ-positive Markov chains

Boucherie, R. J. & van Doorn, E. A., 1998, In : Communications in statistics : Stochastic models. 14, 1/2, p. 171-186 15 p., 10.1080/15326349808807465.

Research output: Contribution to journalArticleAcademicpeer-review

1997
16 Citations (Scopus)
106 Downloads (Pure)

Limiting conditional distributions for birth-death processes

Kijima, M., Nair, M. G., Pollett, P. K. & van Doorn, E. A., 1997, In : Advances in applied probability. 29, 29, p. 185-204 20 p., 10.2307/1427866.

Research output: Contribution to journalArticleAcademicpeer-review

File
1 Citation (Scopus)
28 Downloads (Pure)

Weak convergence of conditioned birth-death processes in discrete time

Coolen-Schrijner, P. & van Doorn, E. A., 1997, In : Journal of applied probability. 34, 34, p. 46-53 12 p.

Research output: Contribution to journalArticleAcademicpeer-review

File
Birth-death Process
Weak Convergence
Discrete-time
Limiting Behavior
Transition Probability
1996

Limit theorems for discrete-time Markov chains on the nonnegative integers conditioned on recurrence to zero

van Doorn, E. A. & Coolen-Schrijner, P., 1996, In : Communications in statistics : Stochastic models. 12, p. 77-102 26 p.

Research output: Contribution to journalArticleAcademicpeer-review

1995
27 Downloads (Pure)

Geometric ergodicity and quasi-stationarity in discrete-time birth-death processes

van Doorn, E. A. & Schrijner, P., 1995, In : Journal of the Australian Mathematical Society. Series B, Applied mathematics. 37, p. 121-144 24 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Geometric Ergodicity
Birth-death Process
Stationarity
Discrete-time
Decay
16 Citations (Scopus)
26 Downloads (Pure)

Ratio limits and limiting conditional distributions for discrete-time birth-death processes

van Doorn, E. A. & Schrijner, P., 1995, In : Journal of mathematical analysis and applications. 190, 1, p. 263-284 22 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Birth-death Process
Conditional Distribution
Limiting Distribution
Discrete-time
Transition Probability
1 Citation (Scopus)
37 Downloads (Pure)

Some new results for chain-sequence polynomials

van Doorn, E. A., 1995, In : Journal of computational and applied mathematics. 57, 1-2, p. 309-317 9 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Polynomials
Polynomial
Orthogonal Polynomials
Moment Sequence
Signed Measure
41 Downloads (Pure)

Weighted sums of orthogonal polynomials with positive zeros

Kijima, M. & van Doorn, E. A., 1995, In : Journal of computational and applied mathematics. 65, 1-3, p. 195-206

Research output: Contribution to journalArticleAcademic

Open Access
File
Weighted Sums
Orthogonal Polynomials
Polynomials
Zero
Polynomial
1994
28 Citations (Scopus)
49 Downloads (Pure)

Blocking probabilities in a loss system with arrivals in geometrically distributed batches and heterogeneous service requirements

van Doorn, E. A. & Panken, F. J. M., 1994, In : IEEE/ACM transactions on networking. 1993, 1, p. 664-667 4 p.

Research output: Contribution to journalArticleAcademicpeer-review

File
1993
11 Citations (Scopus)
29 Downloads (Pure)

Random walk polynomials and random walk measures

van Doorn, E. A. & Schrijner, P., 1993, In : Journal of computational and applied mathematics. 1993, 49, p. 289-296 8 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Random walk
Polynomials
Polynomial
Markov processes
Recurrence relation
1991

Convexity of functions which are generalizations of the Erlang Loss Function and the Erlang Delay Function

Jagers, A. A. & van Doorn, E. A., 1 Sep 1991, In : SIAM review. p. 281-282

Research output: Contribution to journalArticlePopular

Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes

van Doorn, E. A., 1991, In : Advances in applied probability. 2, 23, p. 683-700 18 p.

Research output: Contribution to journalArticleAcademicpeer-review

1990
4 Citations (Scopus)
36 Downloads (Pure)

Analysis of a queuing model for slotted ring networks

van Arem, B. & van Doorn, E. A., 1990, In : Computer networks and ISDN systems. 20, 1-5, p. 309-314 6 p.

Research output: Contribution to journalArticleAcademicpeer-review

File
Local area networks
Computer systems
Servers
Network protocols
1988
33 Citations (Scopus)
62 Downloads (Pure)

Conditional PASTA

van Doorn, E. A. & Regterschot, G. J. K., 1988, In : Operations research letters. 71, 5, p. 229-232

Research output: Contribution to journalArticleAcademic

File