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Barbour, Andrew D.

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Author ID: barbour.andrew-d Recent zbMATH articles by "Barbour, Andrew D."
Published as: Barbour, A. D.; Barbour, Andrew D.; Barbour, Andrew; Barbour, Andrew David
Homepage: http://user.math.uzh.ch/barbour/
External Links: MGP · Wikidata · dblp
Documents Indexed: 155 Publications since 1972, including 5 Books
Reviewing Activity: 142 Reviews
all top 5

Co-Authors

30 single-authored
15 Tavaré, Simon
12 Arratia, Richard Alejandro
12 Xia, Aihua
7 Eagleson, G. K.
7 Reinert, Gesine D.
6 Luczak, Malwina J.
5 Chen, Louis Hsiao-Yun
5 Hall, Peter Gavin
4 Brown, Timothy C.
4 Pollett, Philip K.
3 Bichsel, Manuel
3 Gerrard, R. M.
3 Heinzmann, Dominik
3 Janson, Svante
3 Lindvall, Torgny
3 Pugliese, Andrea
3 Röllin, Adrian
3 Torgerson, Paul R.
3 Utev, Sergey
3 Wagner, Andreas
2 Čekanavičius, Vydas
2 Choi, Kwok Pui
2 Chryssaphinou, Ourania
2 Gnedin, Alexander V.
2 Holst, Lars
2 Kafetzaki, Maria
2 Karoński, Michał
2 Klebaner, Fima C.
2 Månsson, Marianne
2 Mcvinish, Ross S.
2 Ross, Nathan
2 Ruciński, Andrzej
2 Schuh, Hans-Jürgen
2 Socoll, Sanda N.
1 Ball, Frank G.
1 Cartwright, Donald I.
1 Chan, Hock Peng
1 Chigansky, Pavel
1 Collevecchio, Andrea
1 Costi, M.
1 Donnelly, John B.
1 Ethier, Stewart N.
1 Ewens, Warren J.
1 Godbole, Anant P.
1 Granovsky, Boris L.
1 Greenwood, Priscilla E.
1 Griffiths, Robert C.
1 Grübel, Rudolf
1 Hamza, Kais
1 Heesterbeek, J. A. P.
1 Isler, Karin
1 Jensen, Jens Ledet
1 Johnson, Oliver Thomas
1 Kälin, Roman
1 Kaspi, Haya
1 Kontoyiannis, Ioannis
1 Kowalski, Emmanuel
1 Loh, Wei-Liem
1 Luchsinger, Christopher James
1 Madiman, Mokshay M.
1 Martin, R. Douglas
1 Nietlispach, Bruno
1 Nikeghbali, Ashkan
1 Novak, Serguei Yu.
1 Pakes, Anthony G.
1 Phatarfod, Ravindra M.
1 Pósfai, Anna
1 Qian, Jinghua
1 Rogers, L. C. G.
1 Roos, Małgorzata
1 Schassberger, Rolf
1 Schatzmann, Evry
1 Schmidt, Volker
1 Siegmund, David O.
1 Wen, Yuting
all top 5

Serials

21 Advances in Applied Probability
14 Journal of Applied Probability
11 Electronic Journal of Probability
9 The Annals of Applied Probability
8 The Annals of Probability
7 Stochastic Processes and their Applications
6 Journal of Mathematical Biology
6 Mathematical Proceedings of the Cambridge Philosophical Society
5 Probability Theory and Related Fields
5 Random Structures & Algorithms
5 Combinatorics, Probability and Computing
4 Bernoulli
3 Mathematical Biosciences
3 Journal of Theoretical Probability
3 Journal of the Royal Statistical Society. Series B
2 Theoretical Population Biology
2 IMA Journal of Mathematics Applied in Medicine and Biology
2 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics
2 Lecture Notes Series. Institute for Mathematical Sciences. National University of Singapore
1 Scandinavian Journal of Statistics
1 Bulletin of Mathematical Biology
1 The Australian Journal of Statistics
1 Biometrical Journal
1 Biometrika
1 Bulletin of the London Mathematical Society
1 Journal of Combinatorial Theory. Series A
1 Journal of Combinatorial Theory. Series B
1 Naval Research Logistics
1 Proceedings of the American Mathematical Society
1 Statistics & Probability Letters
1 Stochastic Analysis and Applications
1 Statistical Science
1 Communications in Statistics. Theory and Methods
1 Elemente der Mathematik
1 Journal of Physics A: Mathematical and General
1 Notices of the American Mathematical Society
1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
1 Stochastics and Stochastics Reports
1 Statistica Sinica
1 Journal of Biological Systems
1 Methodology and Computing in Applied Probability
1 Proceedings of the Cambridge Philosophical Society
1 Lecture Notes in Statistics
1 Oxford Studies in Probability
1 ALEA. Latin American Journal of Probability and Mathematical Statistics
1 International Journal of Biomathematics
1 Biostatistics, Bioinformatics and Biomathematics
1 EMS Monographs in Mathematics

Publications by Year

Citations contained in zbMATH Open

133 Publications have been cited 1,843 times in 1,159 Documents Cited by Year
Poisson approximation. Zbl 0746.60002
Barbour, A. D.; Holst, Lars; Janson, Svante
267
1992
Logarithmic combinatorial structures: A probabilistic approach. Zbl 1040.60001
Arratia, Richard; Barbour, A. D.; Tavaré, Simon
146
2003
On the rate of Poisson convergence. Zbl 0544.60029
Barbour, A. D.; Hall, Peter
83
1984
Stein’s method for diffusion approximations. Zbl 0665.60008
Barbour, A. D.
68
1990
Compound Poisson approximation for nonnegative random variables via Stein’s method. Zbl 0765.60015
Barbour, A. D.; Chen, Louis H. Y.; Loh, Wei-Liem
59
1992
Poisson process approximations for the Ewens sampling formula. Zbl 0756.60006
Arratia, Richard; Barbour, A. D.; Tavaré, Simon
45
1992
Poisson perturbations. Zbl 0949.62015
Barbour, Andrew D.; Xia, Aihua
43
1999
An introduction to Stein’s method. Zbl 1072.62007
Barbour, A. D. (ed.); Chen, Louis H. Y. (ed.)
42
2005
Stein’s method and Poisson process convergence. Zbl 0661.60034
Barbour, A. D.
40
1988
A central limit theorem for decomposable random variables with applications to random graphs. Zbl 0689.05042
Barbour, A. D.; Karoński, Michał; Ruciński, Andrzej
38
1989
Stein’s method and point process approximation. Zbl 0765.60043
Barbour, A. D.; Brown, T. C.
35
1992
On a functional central limit theorem for Markov population processes. Zbl 0279.60074
Barbour, Andrew D.
32
1974
Compound Poisson approximation: A user’s guide. Zbl 1018.60051
Barbour, A. D.; Chryssaphinou, O.
31
2001
Total variation asymptotics for sums of independent integer random variables. Zbl 1018.60049
Barbour, A. D.; Čekanavičius, V.
30
2002
Quasi-stationary distributions in Markov population processes. Zbl 0337.60069
Barbour, Andrew D.
29
1976
Poisson approximation for some statistics based on exchangeable trials. Zbl 0511.60025
Barbour, A. D.; Eagleson, G. K.
28
1983
Asymptotic expansions in the Poisson limit theorem. Zbl 0622.60049
Barbour, A. D.
24
1987
Networks of queues and the method of stages. Zbl 0342.60065
Barbour, Andrew D.
24
1976
Poisson convergence and random graphs. Zbl 0498.60016
Barbour, A. D.
24
1982
Local and tail approximations near the Poisson limit. Zbl 0674.60022
Barbour, A. D.; Jensen, J. L.
22
1989
Approximating the epidemic curve. Zbl 1301.92072
Barbour, Andrew David; Reinert, Gesine
22
2013
Asymptotic expansions based on smooth functions in the central limit theorem. Zbl 0572.60029
Barbour, A. D.
20
1986
Solving the Stein equation in compound Poisson approximation. Zbl 0982.62007
Barbour, A. D.; Utev, Sergey
18
1998
Small worlds. Zbl 0988.60100
Barbour, A. D.; Reinert, Gesine
18
2001
The principle of the diffusion of arbitrary constants. Zbl 0241.60070
Barbour, Andrew D.
18
1972
Limits of logarithmic combinatorial structures. Zbl 1044.60003
Arratia, R.; Barbour, A. D.; Tavaré, S.
17
2000
Poisson convergence for dissociated statistics. Zbl 0567.62062
Barbour, A. D.; Eagleson, G. K.
17
1984
The duration of the closed stochastic epidemic. Zbl 0307.92014
Barbour, Andrew D.
16
1975
Multiple comparisons and sums of dissociated random variables. Zbl 0559.60027
Barbour, A. D.; Eagleson, G. K.
16
1985
On random polynomials over finite fields. Zbl 0789.60034
Arratia, Richard; Barbour, A. D.; Tavaré, Simon
15
1993
A transition function expansion for a diffusion model with selection. Zbl 1171.60368
Barbour, A. D.; Ethier, S. N.; Griffiths, R. C.
15
2000
Compound Poisson process approximation. Zbl 1033.60059
Barbour, A. D.; Månsson, Marianne
14
2002
Some applications of the Stein-Chen method for proving Poisson convergence. Zbl 0673.60023
Barbour, A. D.; Holst, Lars
14
1989
On the asymptotic behaviour of branching processes with infinite mean. Zbl 0391.60083
Schuh, H.-J.; Barbour, A. D.
14
1977
Compound Poisson approximation in total variation. Zbl 0991.62008
Barbour, A. D.; Utev, Sergey
13
1999
Asymptotic behavior of a metapopulation model. Zbl 1137.37331
Barbour, A. D.; Pugliese, A.
13
2005
Equilibrium distributions Markov population processes. Zbl 0434.60084
Barbour, A. D.
13
1980
Normal approximation for random sums. Zbl 1106.60029
Barbour, A. D.; Xia, Aihua
13
2006
On Stein’s factors for Poisson approximation in Wasserstein distance. Zbl 1328.62076
Barbour, A. D.; Xia, Aihua
13
2006
Total variation approximation for quasi-stationary distributions. Zbl 1213.60126
Barbour, A. D.; Pollett, P. K.
12
2010
Regenerative compositions in the case of slow variation. Zbl 1114.60030
Barbour, A. D.; Gnedin, A. V.
11
2006
Poisson approximation for unbounded functions. I: Independent summands. Zbl 0826.60024
Barbour, A. D.; Chen, Louis H. Y.; Choi, K. P.
11
1995
The number of two-dimensional maxima. Zbl 1005.60028
Barbour, A. D.; Xia, A.
11
2001
Random combinatorial structures: the convergent case. Zbl 1065.60143
Barbour, A. D.; Granovsky, Boris L.
11
2005
Small counts in the infinite occupancy scheme. Zbl 1189.60048
Barbour, A. D.; Gnedin, A. V.
11
2009
Escape from the boundary in Markov population processes. Zbl 1355.92085
Barbour, A. D.; Hamza, K.; Kaspi, Haya; Klebaner, F. C.
10
2015
A host-parasite model yielding heterogeneous parasite loads. Zbl 0853.92020
Barbour, A. D.; Kafetzaki, Maria
10
1993
Compound Poisson approximation for the distribution of extremes. Zbl 1005.60065
Barbour, A. D.; Novak, S. Y.; Xia, A.
10
2002
A stochastic model for the transmission of bilharzia. Zbl 0377.92013
Barbour, A. D.
10
1978
Density dependent Markov population processes. Zbl 0463.60068
Barbour, A. D.
10
1980
Reversing the Berry-Esseen inequality. Zbl 0527.60021
Hall, Peter; Barbour, A. D.
10
1984
Random combinatorial structures and prime factorizations. Zbl 0915.60011
Arratia, Richard; Barbour, A. D.; Tavaré, Simon
9
1997
Tail sums of convergent series of independent random variables. Zbl 0279.60033
Barbour, Andrew D.
9
1974
Translated Poisson approximation for Markov chains. Zbl 1128.60015
Barbour, A. D.; Lindvall, Torgny
9
2006
Compound Poisson approximation in systems reliability. Zbl 0871.90034
Barbour, A. D.; Chryssaphinou, Ourania; Roos, Małgorzata
9
1996
Approximating the Reed-Frost epidemic process. Zbl 1113.92054
Barbour, A. D.; Utev, Sergey
8
2004
Estimating Stein’s constants for compound Poisson approximation. Zbl 0959.62014
Barbour, A. D.; Xia, Aihua
8
2000
Insensitive average residence times in generalized semi-Markov processes. Zbl 0479.60087
Barbour, A. D.; Schassberger, R.
8
1981
A rate for the Erdős-Turán law. Zbl 0805.60008
Barbour, A. D.; Tavaré, Simon
7
1994
Convergence of a structured metapopulation model to Levins’s model. Zbl 1055.92039
Barbour, A. D.; Pugliese, A.
7
2004
Iterates of expanding maps. Zbl 0976.37019
Barbour, A. D.; Gerrard, R. M.; Reinert, G.
7
2000
The Stein-Chen method, point processes and compensators. Zbl 0770.60052
Barbour, A. D.; Brown, Timothy C.
7
1992
A functional combinatorial central limit theorem. Zbl 1193.60010
Barbour, Andrew D.; Janson, Svante
7
2009
Total variation approximation for quasi-equilibrium distributions. II. Zbl 1251.60060
Barbour, A. D.; Pollett, P. K.
7
2012
Stein’s method and the Berry-Esséen theorem. Zbl 0547.60031
Barbour, A. D.; Hall, Peter
7
1984
Laws of large numbers for epidemic models with countably many types. Zbl 1197.92039
Barbour, A. D.; Luczak, M. J.
6
2008
Topics in Poisson approximation. Zbl 0981.60021
Barbour, A. D.
6
2001
Poisson approximation for some epidemic models. Zbl 0753.60013
Ball, Frank; Barbour, A. D.
6
1990
The asymptotic behaviour of birth and death and some related processes. Zbl 0306.60054
Barbour, Andrew D.
6
1975
The uniqueness of Atkinson and Reuter’s epidemic waves. Zbl 0358.92012
Barbour, Andrew D.
6
1977
Compound Poisson approximation via information functionals. Zbl 1225.60037
Barbour, A. D.; Johnson, Oliver; Kontoyiannis, Ioannis; Madiman, Mokshay
6
2010
Discrete small world networks. Zbl 1184.90027
Barbour, Andrew D.; Reinert, Gesine D.
6
2006
Asymptotic behaviour of gossip processes and small-world networks. Zbl 1308.60107
Barbour, A. D.; Reinert, G.
5
2013
Point processes in time and Stein’s method. Zbl 0924.60020
Barbour, A. D.; Brown, Timothy C.; Xia, Aihua
5
1998
Multivariate approximation in total variation. II: Discrete normal approximation. Zbl 1393.62008
Barbour, A. D.; Luczak, M. J.; Xia, A.
5
2018
On Stein’s method and perturbations. Zbl 1121.62016
Barbour, A. D.; Čekanavičius, Vydas; Xia, Aihua
5
2007
Mod-discrete expansions. Zbl 1416.62131
Barbour, A. D.; Kowalski, E.; Nikeghbali, A.
4
2014
On the emergence of random initial conditions in fluid limits. Zbl 1356.60053
Barbour, A. D.; Chigansky, P.; Klebaner, F. C.
4
2016
Coupling a branching process to an infinite dimensional epidemic process. Zbl 1208.92061
Barbour, Andrew D.
4
2010
Approximate versions of Melamed’s theorem. Zbl 0855.60091
Barbour, A. D.; Brown, Timothy C.
4
1996
The Poisson-Dirichlet distribution and the scale-invariant Poisson process. Zbl 0945.60010
Arratia, Richard; Barbour, A. D.; Tavaré, Simon
4
1999
On the binary expansion of a random integer. Zbl 0809.60024
Barbour, A. D.; Chen, L. H. Y.
4
1992
Multivariate approximation in total variation. I: Equilibrium distributions of Markov jump processes. Zbl 1393.62007
Barbour, A. D.; Luczak, M. J.; Xia, A.
4
2018
Approximation by the Dickman distribution and quasi-log arithmic combinatorial structures. Zbl 1225.60018
Barbour, Andrew D.; Nietlispach, Bruno
4
2011
Error bounds in local limit theorems using Stein’s method. Zbl 07049400
Barbour, A. D.; Röllin, Adrian; Ross, Nathan
4
2019
Connecting deterministic and stochastic metapopulation models. Zbl 1350.92039
Barbour, A. D.; McVinish, R.; Pollett, P. K.
3
2015
On sequential versions of the generalized likelihood ratio test. Zbl 0409.62073
Barbour, Andrew D.
3
1979
Second order limit theorems for the Markov branching process in random environments. Zbl 0317.60036
Barbour, Andrew D.
3
1976
Threshold phenomena in epidemic theory. Zbl 0858.92026
Barbour, A. D.
3
1994
A non-uniform bound for translated {P}oisson approximation. Zbl 1064.60034
Barbour, A. D.; Choi, Kwok Pui
3
2004
Stein’s method and applications. A program in honor of Charles Stein. Proceedings of a workshop, Singapore, 28 July – 31 August 2003. Zbl 1094.62017
Barbour, A. D. (ed.); Chen, Louis H. Y. (ed.)
3
2005
Exploiting the Feller coupling for the Ewens sampling formula. Zbl 1442.60009
Arratia, Richard; Barbour, A. D.; Tavaré, Simon
3
2016
Random association of symmetric arrays. Zbl 0619.60014
Barbour, A. D.; Eagleson, G. K.
3
1986
A note on the maximum size of a closed epidemic. Zbl 0309.60058
Barbour, Andrew D.
3
1975
Small cliques in random graphs. Zbl 0733.05050
Barbour, A. D.; Janson, Svante; Karoński, Michał; Ruciński, Andrzej
3
1990
A tale of three couplings: Poisson-Dirichlet and GEM approximations for random permutations. Zbl 1086.60005
Arratia, Richard; Barbour, A. D.; Tavaré, Simon
3
2006
Limit theorems for the simple branching process allowing immigration, II. The case of infinite offspring mean. Zbl 0401.60078
Barbour, A. D.; Pakes, Anthony G.
3
1979
Generalized semi-Markov schemes and open queueing networks. Zbl 0481.60085
Barbour, A. D.
3
1982
The early phase of a bacterial insertion sequence infection. Zbl 1403.92059
Bichsel, Manuel; Barbour, Andrew D.; Wagner, Andreas
3
2010
Central limit approximations for Markov population processes with countably many types. Zbl 1284.92079
Barbour, Andrew; Luczak, Malwina
3
2012
Error bounds in local limit theorems using Stein’s method. Zbl 07049400
Barbour, A. D.; Röllin, Adrian; Ross, Nathan
4
2019
Central limit theorems in the configuration model. Zbl 1466.60039
Barbour, A. D.; Röllin, Adrian
3
2019
Multivariate approximation in total variation using local dependence. Zbl 1467.60018
Barbour, A. D.; Xia, A.
1
2019
Multivariate approximation in total variation. II: Discrete normal approximation. Zbl 1393.62008
Barbour, A. D.; Luczak, M. J.; Xia, A.
5
2018
Multivariate approximation in total variation. I: Equilibrium distributions of Markov jump processes. Zbl 1393.62007
Barbour, A. D.; Luczak, M. J.; Xia, A.
4
2018
Simulating the component counts of combinatorial structures. Zbl 1405.92158
Arratia, Richard; Barbour, A. D.; Ewens, W. J.; Tavaré, Simon
1
2018
General random walk in a random environment defined on Galton-Watson trees. Zbl 1382.60124
Barbour, A. D.; Collevecchio, Andrea
2
2017
On the emergence of random initial conditions in fluid limits. Zbl 1356.60053
Barbour, A. D.; Chigansky, P.; Klebaner, F. C.
4
2016
Exploiting the Feller coupling for the Ewens sampling formula. Zbl 1442.60009
Arratia, Richard; Barbour, A. D.; Tavaré, Simon
3
2016
Escape from the boundary in Markov population processes. Zbl 1355.92085
Barbour, A. D.; Hamza, K.; Kaspi, Haya; Klebaner, F. C.
10
2015
Connecting deterministic and stochastic metapopulation models. Zbl 1350.92039
Barbour, A. D.; McVinish, R.; Pollett, P. K.
3
2015
Individual and patch behaviour in structured metapopulation models. Zbl 1334.92327
Barbour, A. D.; Luczak, M. J.
2
2015
Stein factors for negative binomial approximation in Wasserstein distance. Zbl 1329.62077
Barbour, A. D.; Gan, H. L.; Xia, A.
2
2015
Mod-discrete expansions. Zbl 1416.62131
Barbour, A. D.; Kowalski, E.; Nikeghbali, A.
4
2014
Approximating the epidemic curve. Zbl 1301.92072
Barbour, Andrew David; Reinert, Gesine
22
2013
Asymptotic behaviour of gossip processes and small-world networks. Zbl 1308.60107
Barbour, A. D.; Reinert, G.
5
2013
Estimating the fitness effect of an insertion sequence. Zbl 1256.92036
Bichsel, Manuel; Barbour, A. D.; Wagner, Andreas
2
2013
Total variation approximation for quasi-equilibrium distributions. II. Zbl 1251.60060
Barbour, A. D.; Pollett, P. K.
7
2012
Central limit approximations for Markov population processes with countably many types. Zbl 1284.92079
Barbour, Andrew; Luczak, Malwina
3
2012
A law of large numbers approximation for Markov population processes with countably many types. Zbl 1395.60083
Barbour, A. D.; Luczak, M. J.
3
2012
Probability approximations and beyond. Papers based on the presentations at the conference, Singapore, June 25–26, 2010 to honor Louis Chen on his 70th birthday. Zbl 1230.60007
Barbour, Andrew D.; Chan, Hock Peng; Siegmund, David
1
2012
Approximation by the Dickman distribution and quasi-log arithmic combinatorial structures. Zbl 1225.60018
Barbour, Andrew D.; Nietlispach, Bruno
4
2011
A mechanistic individual-based two-host interaction model for the transmission of a parasitic disease. Zbl 1297.92076
Heinzmann, Dominik; Barbour, A. D.; Torgerson, Paul R.
1
2011
The shortest distance in random multi-type intersection graphs. Zbl 1231.05081
Barbour, A. D.; Reinert, G.
1
2011
Total variation approximation for quasi-stationary distributions. Zbl 1213.60126
Barbour, A. D.; Pollett, P. K.
12
2010
Compound Poisson approximation via information functionals. Zbl 1225.60037
Barbour, A. D.; Johnson, Oliver; Kontoyiannis, Ioannis; Madiman, Mokshay
6
2010
Coupling a branching process to an infinite dimensional epidemic process. Zbl 1208.92061
Barbour, Andrew D.
4
2010
The early phase of a bacterial insertion sequence infection. Zbl 1403.92059
Bichsel, Manuel; Barbour, Andrew D.; Wagner, Andreas
3
2010
Translated Poisson approximation to equilibrium distributions of Markov population processes. Zbl 1214.60041
Socoll, Sanda N.; Barbour, A. D.
2
2010
Assessing molecular variability in cancer genomes. Zbl 1402.92230
Barbour, Andrew D.; Tavaré, Simon
1
2010
Small counts in the infinite occupancy scheme. Zbl 1189.60048
Barbour, A. D.; Gnedin, A. V.
11
2009
A functional combinatorial central limit theorem. Zbl 1193.60010
Barbour, Andrew D.; Janson, Svante
7
2009
Local limit approximations for Markov population processes. Zbl 1195.60114
Socoll, Sanda N.; Barbour, A. D.
1
2009
Laws of large numbers for epidemic models with countably many types. Zbl 1197.92039
Barbour, A. D.; Luczak, M. J.
6
2008
On Stein’s method and perturbations. Zbl 1121.62016
Barbour, A. D.; Čekanavičius, Vydas; Xia, Aihua
5
2007
Normal approximation for random sums. Zbl 1106.60029
Barbour, A. D.; Xia, Aihua
13
2006
On Stein’s factors for Poisson approximation in Wasserstein distance. Zbl 1328.62076
Barbour, A. D.; Xia, Aihua
13
2006
Regenerative compositions in the case of slow variation. Zbl 1114.60030
Barbour, A. D.; Gnedin, A. V.
11
2006
Translated Poisson approximation for Markov chains. Zbl 1128.60015
Barbour, A. D.; Lindvall, Torgny
9
2006
Discrete small world networks. Zbl 1184.90027
Barbour, Andrew D.; Reinert, Gesine D.
6
2006
A tale of three couplings: Poisson-Dirichlet and GEM approximations for random permutations. Zbl 1086.60005
Arratia, Richard; Barbour, A. D.; Tavaré, Simon
3
2006
An introduction to Stein’s method. Zbl 1072.62007
Barbour, A. D.; Chen, Louis H. Y.
42
2005
Asymptotic behavior of a metapopulation model. Zbl 1137.37331
Barbour, A. D.; Pugliese, A.
13
2005
Random combinatorial structures: the convergent case. Zbl 1065.60143
Barbour, A. D.; Granovsky, Boris L.
11
2005
Stein’s method and applications. A program in honor of Charles Stein. Proceedings of a workshop, Singapore, 28 July – 31 August 2003. Zbl 1094.62017
Barbour, A. D.; Chen, Louis H. Y.
3
2005
Approximating the Reed-Frost epidemic process. Zbl 1113.92054
Barbour, A. D.; Utev, Sergey
8
2004
Convergence of a structured metapopulation model to Levins’s model. Zbl 1055.92039
Barbour, A. D.; Pugliese, A.
7
2004
A non-uniform bound for translated {P}oisson approximation. Zbl 1064.60034
Barbour, A. D.; Choi, Kwok Pui
3
2004
Logarithmic combinatorial structures: A probabilistic approach. Zbl 1040.60001
Arratia, Richard; Barbour, A. D.; Tavaré, Simon
146
2003
Total variation asymptotics for sums of independent integer random variables. Zbl 1018.60049
Barbour, A. D.; Čekanavičius, V.
30
2002
Compound Poisson process approximation. Zbl 1033.60059
Barbour, A. D.; Månsson, Marianne
14
2002
Compound Poisson approximation for the distribution of extremes. Zbl 1005.60065
Barbour, A. D.; Novak, S. Y.; Xia, A.
10
2002
Compound Poisson approximation: A user’s guide. Zbl 1018.60051
Barbour, A. D.; Chryssaphinou, O.
31
2001
Small worlds. Zbl 0988.60100
Barbour, A. D.; Reinert, Gesine
18
2001
The number of two-dimensional maxima. Zbl 1005.60028
Barbour, A. D.; Xia, A.
11
2001
Topics in Poisson approximation. Zbl 0981.60021
Barbour, A. D.
6
2001
On Laslett’s transform for the Boolean model. Zbl 0978.60017
Barbour, A. D.; Schmidt, V.
1
2001
Limits of logarithmic combinatorial structures. Zbl 1044.60003
Arratia, R.; Barbour, A. D.; Tavaré, S.
17
2000
A transition function expansion for a diffusion model with selection. Zbl 1171.60368
Barbour, A. D.; Ethier, S. N.; Griffiths, R. C.
15
2000
Estimating Stein’s constants for compound Poisson approximation. Zbl 0959.62014
Barbour, A. D.; Xia, Aihua
8
2000
Iterates of expanding maps. Zbl 0976.37019
Barbour, A. D.; Gerrard, R. M.; Reinert, G.
7
2000
Compound Poisson approximation and the clustering of random points. Zbl 1057.60018
Barbour, A. D.; Månsson, Marianne
2
2000
On the variance-to-mean ratio in models of parasite distributions. Zbl 0964.92038
Barbour, Andrew D.; Pugliese, Andrea
2
2000
The number of components in a logarithmic combinatorial structure. Zbl 1056.60012
Arratis, Richard; Barbour, A. D.; Tavaré, Simon
1
2000
Poisson perturbations. Zbl 0949.62015
Barbour, Andrew D.; Xia, Aihua
43
1999
Compound Poisson approximation in total variation. Zbl 0991.62008
Barbour, A. D.; Utev, Sergey
13
1999
The Poisson-Dirichlet distribution and the scale-invariant Poisson process. Zbl 0945.60010
Arratia, Richard; Barbour, A. D.; Tavaré, Simon
4
1999
On Poisson-Dirichlet limits for random decomposable combinatorial structures. Zbl 0938.60019
Arratia, Richard; Barbour, A. D.; Tavaré, Simon
2
1999
Solving the Stein equation in compound Poisson approximation. Zbl 0982.62007
Barbour, A. D.; Utev, Sergey
18
1998
Point processes in time and Stein’s method. Zbl 0924.60020
Barbour, A. D.; Brown, Timothy C.; Xia, Aihua
5
1998
Random combinatorial structures and prime factorizations. Zbl 0915.60011
Arratia, Richard; Barbour, A. D.; Tavaré, Simon
9
1997
Imperfections in random tournaments. Zbl 0867.05060
Barbour, A. D.; Godbole, Anant P.; Qian, Jinghua
1
1997
Compound Poisson approximation in systems reliability. Zbl 0871.90034
Barbour, A. D.; Chryssaphinou, Ourania; Roos, Małgorzata
9
1996
Approximate versions of Melamed’s theorem. Zbl 0855.60091
Barbour, A. D.; Brown, Timothy C.
4
1996
Thresholds and initial growth rates in a model of parasitic infection. Zbl 0871.92024
Barbour, A. D.; Heesterbeek, J. A. P.; Luchsinger, C. J.
1
1996
Poisson approximation for unbounded functions. I: Independent summands. Zbl 0826.60024
Barbour, A. D.; Chen, Louis H. Y.; Choi, K. P.
11
1995
The first divisible sum. Zbl 0814.60084
Barbour, A. D.; Grübel, R.
2
1995
A rate for the Erdős-Turán law. Zbl 0805.60008
Barbour, A. D.; Tavaré, Simon
7
1994
Threshold phenomena in epidemic theory. Zbl 0858.92026
Barbour, A. D.
3
1994
On random polynomials over finite fields. Zbl 0789.60034
Arratia, Richard; Barbour, A. D.; Tavaré, Simon
15
1993
A host-parasite model yielding heterogeneous parasite loads. Zbl 0853.92020
Barbour, A. D.; Kafetzaki, Maria
10
1993
Rates of Poisson approximation to finite range random fields. Zbl 0784.60053
Barbour, A. D.; Greenwood, P. E.
2
1993
Poisson approximation. Zbl 0746.60002
Barbour, A. D.; Holst, Lars; Janson, Svante
267
1992
Compound Poisson approximation for nonnegative random variables via Stein’s method. Zbl 0765.60015
Barbour, A. D.; Chen, Louis H. Y.; Loh, Wei-Liem
59
1992
Poisson process approximations for the Ewens sampling formula. Zbl 0756.60006
Arratia, Richard; Barbour, A. D.; Tavaré, Simon
45
1992
Stein’s method and point process approximation. Zbl 0765.60043
Barbour, A. D.; Brown, T. C.
35
1992
The Stein-Chen method, point processes and compensators. Zbl 0770.60052
Barbour, A. D.; Brown, Timothy C.
7
1992
On the binary expansion of a random integer. Zbl 0809.60024
Barbour, A. D.; Chen, L. H. Y.
4
1992
Refined approximations for the Ewens sampling formula. Zbl 0798.60010
Barbour, A. D.
2
1992
Modeling the overdispersion of parasite loads. Zbl 0739.92013
Barbour, A. D.; Kafetzaki, Maria
2
1991
Stochastic ordering of order statistics. Zbl 0729.62048
Barbour, A. D.; Lindvall, T.; Rogers, L. C. G.
2
1991
Stein’s method for diffusion approximations. Zbl 0665.60008
Barbour, A. D.
68
1990
Poisson approximation for some epidemic models. Zbl 0753.60013
Ball, Frank; Barbour, A. D.
6
1990
Small cliques in random graphs. Zbl 0733.05050
Barbour, A. D.; Janson, Svante; Karoński, Michał; Ruciński, Andrzej
3
1990
A central limit theorem for decomposable random variables with applications to random graphs. Zbl 0689.05042
Barbour, A. D.; Karoński, Michał; Ruciński, Andrzej
38
1989
Local and tail approximations near the Poisson limit. Zbl 0674.60022
Barbour, A. D.; Jensen, J. L.
22
1989
Some applications of the Stein-Chen method for proving Poisson convergence. Zbl 0673.60023
Barbour, A. D.; Holst, Lars
14
1989
Stein’s method and Poisson process convergence. Zbl 0661.60034
Barbour, A. D.
40
1988
Asymptotic expansions in the Poisson limit theorem. Zbl 0622.60049
Barbour, A. D.
24
1987
An improved Poisson limit theorem for sums of dissociated random variables. Zbl 0629.60026
Barbour, A. D.; Eagleson, G. K.
2
1987
...and 33 more Documents
all top 5

Cited by 1,224 Authors

48 Barbour, Andrew D.
32 Čekanavičius, Vydas
29 Xia, Aihua
28 Janson, Svante
18 Manstavičius, Eugenijus
18 Röllin, Adrian
16 Pollett, Philip K.
13 Roos, Bero
11 Gaunt, Robert Edward
11 Gnedin, Alexander V.
11 Goldstein, Larry
11 Ross, Nathan
11 Sunklodas, Jonas Kazys
10 Godbole, Anant P.
10 Luczak, Malwina J.
10 Neal, Peter J.
10 Reinert, Gesine D.
9 Adell, José Antonio
9 Ball, Frank G.
9 Deheuvels, Paul
9 Marynych, Alexander V.
9 Neammanee, Kritsana
9 Ross, Joshua V.
9 Vellaisamy, Palaniappan
9 Zeindler, Dirk
8 Chen, Louis Hsiao-Yun
8 Diaconis, Persi Warren
8 Griffiths, Robert C.
8 Iksanov, Aleksander M.
8 Klebaner, Fima C.
8 Mcvinish, Ross S.
8 Pitman, Jim William
8 Tavaré, Simon
8 Yukich, Joseph Elliott
7 Arratia, Richard Alejandro
7 Brown, Timothy C.
7 Decreusefond, Laurent
7 Durrett, Richard Timothy
7 Fulman, Jason E.
7 Granovsky, Boris L.
7 Holst, Lars
7 Koutras, Markos V.
7 Nikeghbali, Ashkan
7 Peccati, Giovanni
7 Prieur, Clémentine
7 Schuhmacher, Dominic
6 Berestycki, Nathanaël
6 Bollobás, Béla
6 Fang, Xiao
6 Fu, James C.
6 Nourdin, Ivan
6 Novak, Serguei Yu.
6 Pakes, Anthony G.
6 Peköz, Erol A.
6 Pfeifer, Dietmar
6 Swan, Yvik C.
6 van Dijk, Nico M.
5 Bogachev, Leonid V.
5 Boutsikas, Michael V.
5 Britton, Tom
5 Chebunin, Mikhail Georgievich
5 Daly, Fraser
5 Diekmann, Odo
5 Erhardsson, Torkel
5 Glaz, Joseph
5 Lekuona, Alberto
5 Leung, Ka Yin
5 Shao, Qi-Man
5 Teerapabolarn, Kanint
5 Yakymiv, Arsen Lubomirovich
4 Alsmeyer, Gerold
4 Berckmoes, Ben
4 Borisov, Igor S.
4 Chatterjee, Sourav
4 Chigansky, Pavel
4 Eichelsbacher, Peter
4 Fathi, Max
4 Ganesh, Ayalvadi J.
4 House, Thomas
4 Hwang, Hsien-Kuei
4 Jagers, Peter
4 Lefèvre, Claude
4 Leonenko, Nikolai N.
4 Privault, Nicolas
4 Pugliese, Andrea
4 Ruciński, Andrzej
4 Ruzankin, Pavel S.
4 Sethuraman, Sunder
4 Stark, Dudley
4 Utev, Sergey
4 van der Hofstad, Remco W.
4 Watson, Ray
4 Yakubovich, Yuri V.
4 Zhang, Fuxi
3 Anoz, José M.
3 Artalejo, Jesus R.
3 Bhamidi, Shankar
3 Burden, Conrad John
3 Castillo-Chavez, Carlos
3 Chen, Jie
...and 1,124 more Authors
all top 5

Cited in 215 Serials

75 Stochastic Processes and their Applications
59 The Annals of Applied Probability
58 Journal of Applied Probability
53 The Annals of Probability
51 Statistics & Probability Letters
45 Bernoulli
41 Lithuanian Mathematical Journal
40 Advances in Applied Probability
35 Journal of Mathematical Biology
35 Mathematical Biosciences
30 Theoretical Population Biology
30 Probability Theory and Related Fields
27 Random Structures & Algorithms
26 Journal of Statistical Planning and Inference
20 Journal of Theoretical Probability
20 Electronic Journal of Probability
19 Journal of Statistical Physics
17 Communications in Statistics. Theory and Methods
17 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
15 Combinatorics, Probability and Computing
11 Journal of Mathematical Analysis and Applications
11 Transactions of the American Mathematical Society
11 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics
10 Discrete Mathematics
8 Journal of Multivariate Analysis
8 Electronic Communications in Probability
8 Methodology and Computing in Applied Probability
7 Mathematical Proceedings of the Cambridge Philosophical Society
7 Annals of the Institute of Statistical Mathematics
7 Discrete Mathematics and Applications
7 Probability Surveys
6 Theory of Probability and its Applications
6 Journal of Combinatorial Theory. Series A
6 Journal of Functional Analysis
6 European Journal of Combinatorics
6 Journal of Mathematical Sciences (New York)
6 ALEA. Latin American Journal of Probability and Mathematical Statistics
5 Discrete Applied Mathematics
5 Israel Journal of Mathematics
5 Journal of Soviet Mathematics
5 Theoretical Computer Science
5 Stochastic Analysis and Applications
5 European Journal of Operational Research
5 Brazilian Journal of Probability and Statistics
4 Bulletin of Mathematical Biology
4 Advances in Applied Mathematics
4 Operations Research Letters
4 Acta Applicandae Mathematicae
4 Queueing Systems
4 Journal of Algebraic Combinatorics
4 Extremes
4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
3 Annales de l’Institut Fourier
3 Journal of Combinatorial Theory. Series B
3 Kybernetika
3 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
3 Insurance Mathematics & Economics
3 Statistics
3 SIAM Journal on Discrete Mathematics
3 Communications in Statistics. Simulation and Computation
3 Journal of Statistical Computation and Simulation
3 Linear Algebra and its Applications
3 Computational Statistics and Data Analysis
3 The Ramanujan Journal
3 Annals of Combinatorics
3 Probability in the Engineering and Informational Sciences
3 Sibirskie Èlektronnye Matematicheskie Izvestiya
3 Electronic Journal of Statistics
3 Nonlinear Analysis. Theory, Methods & Applications
2 The Canadian Journal of Statistics
2 Communications in Mathematical Physics
2 Journal of Mathematical Physics
2 Mathematical Notes
2 Metrika
2 Nonlinearity
2 The Annals of Statistics
2 Applied Mathematics and Computation
2 Automatica
2 Blätter (Deutsche Gesellschaft für Versicherungsmathematik)
2 Journal of Computational and Applied Mathematics
2 Monatshefte für Mathematik
2 Proceedings of the American Mathematical Society
2 Semigroup Forum
2 Siberian Mathematical Journal
2 Statistica Neerlandica
2 Trabajos de Estadistica y de Investigacion Operativa
2 Mathematical and Computer Modelling
2 SIAM Journal on Matrix Analysis and Applications
2 Applications of Mathematics
2 SIAM Journal on Applied Mathematics
2 Bulletin of the American Mathematical Society. New Series
2 Journal of Dynamics and Differential Equations
2 Potential Analysis
2 Journal of Inequalities and Applications
2 The Econometrics Journal
2 CEJOR. Central European Journal of Operations Research
2 Nonlinear Analysis. Modelling and Control
2 Stochastics and Dynamics
2 Journal of the Korean Statistical Society
2 Journal of Biological Dynamics
...and 115 more Serials
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Cited in 46 Fields

937 Probability theory and stochastic processes (60-XX)
250 Statistics (62-XX)
218 Combinatorics (05-XX)
196 Biology and other natural sciences (92-XX)
46 Operations research, mathematical programming (90-XX)
39 Statistical mechanics, structure of matter (82-XX)
36 Numerical analysis (65-XX)
34 Number theory (11-XX)
31 Computer science (68-XX)
30 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
24 Dynamical systems and ergodic theory (37-XX)
20 Linear and multilinear algebra; matrix theory (15-XX)
18 Group theory and generalizations (20-XX)
18 Ordinary differential equations (34-XX)
12 Information and communication theory, circuits (94-XX)
11 Operator theory (47-XX)
7 Partial differential equations (35-XX)
7 Functional analysis (46-XX)
6 Integral equations (45-XX)
6 Convex and discrete geometry (52-XX)
6 Systems theory; control (93-XX)
5 History and biography (01-XX)
5 Measure and integration (28-XX)
5 Approximations and expansions (41-XX)
4 Field theory and polynomials (12-XX)
4 Real functions (26-XX)
4 Special functions (33-XX)
3 General and overarching topics; collections (00-XX)
3 Sequences, series, summability (40-XX)
3 Integral transforms, operational calculus (44-XX)
3 Calculus of variations and optimal control; optimization (49-XX)
2 Order, lattices, ordered algebraic structures (06-XX)
2 Functions of a complex variable (30-XX)
2 Harmonic analysis on Euclidean spaces (42-XX)
2 Abstract harmonic analysis (43-XX)
2 Relativity and gravitational theory (83-XX)
1 Algebraic geometry (14-XX)
1 Nonassociative rings and algebras (17-XX)
1 Topological groups, Lie groups (22-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Difference and functional equations (39-XX)
1 Algebraic topology (55-XX)
1 Manifolds and cell complexes (57-XX)
1 Global analysis, analysis on manifolds (58-XX)
1 Mechanics of particles and systems (70-XX)
1 Quantum theory (81-XX)

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