## Biggins, J. D.

Compute Distance To:
 Author ID: biggins.j-d Published as: Biggins, J. D. External Links: MGP
 Documents Indexed: 45 Publications since 1976 Co-Authors: 20 Co-Authors with 24 Joint Publications 547 Co-Co-Authors
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### Co-Authors

 21 single-authored 4 D’Souza, J. C. 4 Kyprianou, Andreas E. 2 Bingham, Nicholas Hugh 2 Grey, D. R. 2 Yue, Kelvin K. 1 Alsmeyer, Gerold 1 Cannings, Chris 1 Cohn, Harry 1 Götz, Thomas B. 1 Hambly, Ben M. 1 Jones, Owen Dafydd 1 Lubachevsky, Boris D. 1 Meiners, Matthias 1 Nadarajah, Saralees 1 Nerman, Olle 1 Penman, David B. 1 Rahimzadeh Sani, A. 1 Schwartz, Adam 1 Shanbhag, Damodar N. 1 Weiss, Alan
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### Serials

 8 Advances in Applied Probability 5 Stochastic Processes and their Applications 4 Journal of Applied Probability 3 Teoriya Veroyatnosteĭ i eë Primeneniya 3 The Annals of Probability 3 The Annals of Applied Probability 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 Electronic Communications in Probability 1 Theory of Probability and its Applications 1 The Australian Journal of Statistics 1 British Journal of Mathematical & Statistical Psychology 1 Journal of the London Mathematical Society. Second Series 1 Transactions of the American Mathematical Society 1 Statistics & Probability Letters 1 Communications in Statistics. Stochastic Models 1 Electronic Journal of Probability
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### Fields

 43 Probability theory and stochastic processes (60-XX) 2 Combinatorics (05-XX) 2 Difference and functional equations (39-XX) 2 Statistics (62-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

40 Publications have been cited 834 times in 449 Documents Cited by Year
Martingale convergence in the branching random walk. Zbl 0356.60053
Biggins, J. D.
1977
Measure change in multitype branching. Zbl 1056.60082
Biggins, J. D.; Kyprianou, A. E.
2004
Uniform convergence of martingales in the branching random walk. Zbl 0748.60080
Biggins, J. D.
1992
Chernoff’s theorem in the branching random walk. Zbl 0373.60090
Biggins, J. D.
1977
The first- and last-birth problems for a multitype age-dependent branching process. Zbl 0339.60074
Biggins, J. D.
1976
Seneta-Heyde norming in the branching random walk. Zbl 0873.60062
Biggins, J. D.; Kyprianou, A. E.
1997
Fixed points of the smoothing transform: the boundary case. Zbl 1110.60081
Biggins, J. D.; Kyprianou, A. E.
2005
Large deviations in the supercritical branching process. Zbl 0796.60090
Biggins, J. D.; Bingham, N. H.
1993
The functional equation of the smoothing transform. Zbl 1266.39022
Alsmeyer, Gerold; Biggins, J. D.; Meiners, Matthias
2012
Growth rates in the branching random walk. Zbl 0387.60092
Biggins, J. D.
1979
The central limit theorem for the supercritical branching random walk, and related results. Zbl 0703.60083
Biggins, J. D.
1990
The asymptotic shape of the branching random walk. Zbl 0383.60078
Biggins, J. D.
1978
The growth and spread of the general branching random walk. Zbl 0859.60075
Biggins, J. D.
1995
The supercritical Galton-Watson process in varying environments. Zbl 0758.60088
D’Souza, J. C.; Biggins, J. D.
1992
Lindley-type equations in the branching random walk. Zbl 0933.60087
Biggins, J. D.
1998
How fast does a general branching random walk spread? Zbl 0873.60061
Biggins, J. D.
1997
Near-constancy phenomena in branching processes. Zbl 0749.60077
Biggins, J. D.; Bingham, N. H.
1991
Markov renewal processes, counters and repeated sequences in Markov chains. Zbl 0629.60100
Biggins, J. D.; Cannings, C.
1987
A branching random walk with a barrier. Zbl 0749.60076
Biggins, J. D.; Lubachevsky, Boris D.; Schwartz, Adam; Weiss, Alan
1991
Multi-type branching in varying environment. Zbl 0997.60093
Biggins, J. D.; Cohn, H.; Nerman, O.
1999
Convergence results on multitype, multivariate branching random walks. Zbl 1076.60072
Biggins, J. D.; Rahimzadeh Sani, A.
2005
Continuity of limit random variables in the branching random walk. Zbl 0425.60069
Biggins, J. D.; Grey, D. R.
1979
Uniform convergence of martingales in the one-dimensional branching random walk. Zbl 0770.60077
Biggins, J. D.
1991
Branching out. Zbl 1213.60134
Biggins, J. D.
2010
Multifractal spectra for random self-similar measures via branching processes. Zbl 1223.28010
Biggins, J. D.; Hambly, B. M.; Jones, O. D.
2011
Large deviations for mixtures. Zbl 1060.60026
Biggins, J. D.
2004
A note on the growth of random trees. Zbl 0904.60067
Biggins, J. D.; Grey, D. R.
1997
Random walk conditioned to stay positive. Zbl 1046.60066
Biggins, J. D.
2003
Branching random walk: Seneta-Heyde norming. Zbl 0864.60070
Biggins, J. D.; Kyprianou, A. E.
1996
Near-constancy of the Harris function in the simple branching process. Zbl 0777.60080
1993
Some divisibility problems in branching processes. Zbl 0473.60069
Biggins, J. D.; Shanbhag, D. N.
1981
The supercritical Galton-Watson process in varying environments – Seneta-Heyde norming. Zbl 0789.60064
Biggins, J. D.; D’Souza, J. C.
1993
A note on repeated sequences in Markov chains. Zbl 0634.60083
Biggins, J. D.
1987
Spreading speeds in reducible multitype branching random walk. Zbl 1269.60068
Biggins, J. D.
2012
Spatial spread in branching processes. Zbl 0443.60082
Biggins, J. D.
1980
The growth of iterates of multivariate generating functions. Zbl 1158.39017
Biggins, J. D.
2008
Large deviations in randomly coloured random graphs. Zbl 1185.05125
Biggins, J. D.; Penman, D. B.
2009
Expected population size in the generation-dependent branching process. Zbl 0626.60081
Biggins, J. D.; Götz, Thomas
1987
Martingale convergence and large deviations in branching random walk. Zbl 0787.60105
Biggins, J. D.
1992
Limiting point processes in the branching random walk. Zbl 0447.60065
Biggins, J. D.
1981
The functional equation of the smoothing transform. Zbl 1266.39022
Alsmeyer, Gerold; Biggins, J. D.; Meiners, Matthias
2012
Spreading speeds in reducible multitype branching random walk. Zbl 1269.60068
Biggins, J. D.
2012
Multifractal spectra for random self-similar measures via branching processes. Zbl 1223.28010
Biggins, J. D.; Hambly, B. M.; Jones, O. D.
2011
Branching out. Zbl 1213.60134
Biggins, J. D.
2010
Large deviations in randomly coloured random graphs. Zbl 1185.05125
Biggins, J. D.; Penman, D. B.
2009
The growth of iterates of multivariate generating functions. Zbl 1158.39017
Biggins, J. D.
2008
Fixed points of the smoothing transform: the boundary case. Zbl 1110.60081
Biggins, J. D.; Kyprianou, A. E.
2005
Convergence results on multitype, multivariate branching random walks. Zbl 1076.60072
Biggins, J. D.; Rahimzadeh Sani, A.
2005
Measure change in multitype branching. Zbl 1056.60082
Biggins, J. D.; Kyprianou, A. E.
2004
Large deviations for mixtures. Zbl 1060.60026
Biggins, J. D.
2004
Random walk conditioned to stay positive. Zbl 1046.60066
Biggins, J. D.
2003
Multi-type branching in varying environment. Zbl 0997.60093
Biggins, J. D.; Cohn, H.; Nerman, O.
1999
Lindley-type equations in the branching random walk. Zbl 0933.60087
Biggins, J. D.
1998
Seneta-Heyde norming in the branching random walk. Zbl 0873.60062
Biggins, J. D.; Kyprianou, A. E.
1997
How fast does a general branching random walk spread? Zbl 0873.60061
Biggins, J. D.
1997
A note on the growth of random trees. Zbl 0904.60067
Biggins, J. D.; Grey, D. R.
1997
Branching random walk: Seneta-Heyde norming. Zbl 0864.60070
Biggins, J. D.; Kyprianou, A. E.
1996
The growth and spread of the general branching random walk. Zbl 0859.60075
Biggins, J. D.
1995
Large deviations in the supercritical branching process. Zbl 0796.60090
Biggins, J. D.; Bingham, N. H.
1993
Near-constancy of the Harris function in the simple branching process. Zbl 0777.60080
1993
The supercritical Galton-Watson process in varying environments – Seneta-Heyde norming. Zbl 0789.60064
Biggins, J. D.; D&rsquo;Souza, J. C.
1993
Uniform convergence of martingales in the branching random walk. Zbl 0748.60080
Biggins, J. D.
1992
The supercritical Galton-Watson process in varying environments. Zbl 0758.60088
D&rsquo;Souza, J. C.; Biggins, J. D.
1992
Martingale convergence and large deviations in branching random walk. Zbl 0787.60105
Biggins, J. D.
1992
Near-constancy phenomena in branching processes. Zbl 0749.60077
Biggins, J. D.; Bingham, N. H.
1991
A branching random walk with a barrier. Zbl 0749.60076
Biggins, J. D.; Lubachevsky, Boris D.; Schwartz, Adam; Weiss, Alan
1991
Uniform convergence of martingales in the one-dimensional branching random walk. Zbl 0770.60077
Biggins, J. D.
1991
The central limit theorem for the supercritical branching random walk, and related results. Zbl 0703.60083
Biggins, J. D.
1990
Markov renewal processes, counters and repeated sequences in Markov chains. Zbl 0629.60100
Biggins, J. D.; Cannings, C.
1987
A note on repeated sequences in Markov chains. Zbl 0634.60083
Biggins, J. D.
1987
Expected population size in the generation-dependent branching process. Zbl 0626.60081
Biggins, J. D.; Götz, Thomas
1987
Some divisibility problems in branching processes. Zbl 0473.60069
Biggins, J. D.; Shanbhag, D. N.
1981
Limiting point processes in the branching random walk. Zbl 0447.60065
Biggins, J. D.
1981
Spatial spread in branching processes. Zbl 0443.60082
Biggins, J. D.
1980
Growth rates in the branching random walk. Zbl 0387.60092
Biggins, J. D.
1979
Continuity of limit random variables in the branching random walk. Zbl 0425.60069
Biggins, J. D.; Grey, D. R.
1979
The asymptotic shape of the branching random walk. Zbl 0383.60078
Biggins, J. D.
1978
Martingale convergence in the branching random walk. Zbl 0356.60053
Biggins, J. D.
1977
Chernoff’s theorem in the branching random walk. Zbl 0373.60090
Biggins, J. D.
1977
The first- and last-birth problems for a multitype age-dependent branching process. Zbl 0339.60074
Biggins, J. D.
1976
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### Cited by 454 Authors

 15 Liu, Quansheng 13 Biggins, J. D. 13 Kyprianou, Andreas E. 13 Mallein, Bastien 12 Meiners, Matthias 11 Aidekon, Elie E. F. 11 Barral, Julien 10 Bertoin, Jean 10 Hu, Yueyun 10 Iksanov, Aleksander M. 10 Olvera-Cravioto, Mariana 10 Shi, Zhan 9 Buraczewski, Dariusz 8 Chen, Xinxin 8 Gao, Zhiqiang 8 Harris, Simon C. 7 Alsmeyer, Gerold 7 Durrett, Richard Timothy 7 Maillard, Pascal 7 Ren, Yanxia 6 Attia, Najmeddine 6 Huang, Chunmao 6 Jones, Owen Dafydd 6 Kolesko, Konrad 6 Rouault, Alain 5 Addario-Berry, Louigi 5 Bansaye, Vincent 5 Devroye, Luc P. J. A. 5 Gantert, Nina 5 Hambly, Ben M. 5 Rösler, Uwe 4 Bezborodov, Viktor 4 Chauvin, Brigitte 4 Cohn, Harry 4 Damek, Ewa 4 Di Persio, Luca 4 Engländer, János 4 Hong, Wenming 4 Jelenković, Predrag R. 4 Krüger, Tyll 4 Liang, Xingang 4 Mentemeier, Sebastian 4 Pakes, Anthony G. 4 Powell, Ellen 4 Wachtel, Vitali I. 4 Waymire, Edward C. 4 Zeitouni, Ofer 3 Andreoletti, Pierre 3 Broutin, Nicolas 3 Bulinskaya, Ekaterina Vladimirovna 3 Comets, Francis M. 3 Curien, Nicolas 3 Dyszewski, Piotr 3 Fleischmann, Klaus 3 Giacomin, Giambattista 3 Grabner, Peter J. 3 Gravner, Janko 3 Griffeath, David 3 Griffiths, Simon 3 Grübel, Rudolf 3 He, Hui 3 Janson, Svante 3 Kabluchko, Zakhar A. 3 Kersting, Götz-Dietrich 3 Kortchemski, Igor 3 Li, Yingqiu 3 Liu, Rongli 3 Louidor, Oren 3 Madaule, Thomas 3 Mandjes, Michel Robertus Hendrikus 3 Mörters, Peter 3 Palmowski, Zbigniew 3 Peres, Yuval 3 Pozdnyakov, Vladimir 3 Rhodes, Rémi 3 Shanbhag, Damodar N. 3 Song, Renming 3 Vargas, Vincent 3 Vatutin, Vladimir Alekseevich 3 Watson, Alexander R. 3 Webb, Christian 3 Zhang, Mei 3 Zhang, Xiaoyue 3 Zucca, Fabio 2 Alberts, Tom 2 Aldous, David John 2 Amini, Omid 2 Athreya, Krishna Balasundaram 2 Basdevant, Anne-Laure 2 Basrak, Bojan 2 Berestycki, Julien 2 Bertacchi, Daniela 2 Bhattacharya, Ayan 2 Bocharov, Sergey 2 Borovkov, Konstantin A. 2 Braunsteins, Peter 2 Caliebe, Amke 2 Chu, WeiJuan 2 Dascaliuc, Radu 2 de Raphélis, Loïc ...and 354 more Authors
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### Cited in 102 Serials

 54 Stochastic Processes and their Applications 35 The Annals of Applied Probability 32 The Annals of Probability 28 Journal of Applied Probability 24 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 22 Probability Theory and Related Fields 18 Statistics & Probability Letters 18 Journal of Theoretical Probability 17 Advances in Applied Probability 13 Electronic Communications in Probability 11 Electronic Journal of Probability 11 Bernoulli 9 Journal of Statistical Physics 7 Communications in Mathematical Physics 6 Frontiers of Mathematics in China 5 Transactions of the American Mathematical Society 5 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 5 Queueing Systems 4 Theory of Probability and its Applications 4 Annals of the Institute of Statistical Mathematics 4 Random Structures & Algorithms 4 Brazilian Journal of Probability and Statistics 3 Mathematical Biosciences 3 Combinatorics, Probability and Computing 3 Journal of Difference Equations and Applications 3 Stochastic Models 3 Proceedings of the Steklov Institute of Mathematics 3 ALEA. Latin American Journal of Probability and Mathematical Statistics 3 Science China. Mathematics 2 Acta Informatica 2 Journal of Mathematical Biology 2 Advances in Mathematics 2 Journal of Soviet Mathematics 2 Journal of Statistical Planning and Inference 2 Probability and Mathematical Statistics 2 Revista Matemática Iberoamericana 2 Mathematical and Computer Modelling 2 Science in China. Series A 2 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 2 Infinite Dimensional Analysis, Quantum Probability and Related Topics 2 Annals of Mathematics. Second Series 2 Acta Mathematica Sinica. English Series 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Stochastics 1 Bulletin of the Australian Mathematical Society 1 Communications on Pure and Applied Mathematics 1 Discrete Applied Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 Lithuanian Mathematical Journal 1 Metrika 1 Nonlinearity 1 Periodica Mathematica Hungarica 1 Arkiv för Matematik 1 The Annals of Statistics 1 Geometriae Dedicata 1 Illinois Journal of Mathematics 1 Mathematische Nachrichten 1 Mathematics of Operations Research 1 Mathematika 1 Proceedings of the American Mathematical Society 1 Proceedings of the Japan Academy. Series A 1 Proceedings of the London Mathematical Society. Third Series 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Theoretical Computer Science 1 Theoretical Population Biology 1 Advances in Applied Mathematics 1 Acta Applicandae Mathematicae 1 Journal of the American Mathematical Society 1 Journal of Applied Mathematics and Stochastic Analysis 1 International Journal of Mathematics 1 International Journal of Algebra and Computation 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Geometric and Functional Analysis. GAFA 1 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 1 Communications in Statistics. Theory and Methods 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Computational Statistics and Data Analysis 1 Journal of Nonlinear Science 1 Test 1 Statistical Papers 1 Journal of Mathematical Sciences (New York) 1 Bulletin des Sciences Mathématiques 1 Mathematical Physics, Analysis and Geometry 1 Taiwanese Journal of Mathematics 1 Chaos 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Stochastics and Dynamics 1 Analysis in Theory and Applications 1 Analysis and Applications (Singapore) 1 Journal of Physics A: Mathematical and Theoretical 1 Journal of Statistical Theory and Practice 1 Probability Surveys 1 Stochastic Systems 1 Annales de l’Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD) 1 Modern Stochastics. Theory and Applications ...and 2 more Serials
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### Cited in 33 Fields

 422 Probability theory and stochastic processes (60-XX) 43 Statistical mechanics, structure of matter (82-XX) 40 Combinatorics (05-XX) 26 Measure and integration (28-XX) 25 Biology and other natural sciences (92-XX) 21 Statistics (62-XX) 21 Computer science (68-XX) 17 Partial differential equations (35-XX) 9 Dynamical systems and ergodic theory (37-XX) 7 Numerical analysis (65-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Number theory (11-XX) 5 Difference and functional equations (39-XX) 5 Operator theory (47-XX) 4 Information and communication theory, circuits (94-XX) 3 Operations research, mathematical programming (90-XX) 2 Group theory and generalizations (20-XX) 2 Functions of a complex variable (30-XX) 2 Sequences, series, summability (40-XX) 2 Integral transforms, operational calculus (44-XX) 2 Fluid mechanics (76-XX) 2 Quantum theory (81-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Systems theory; control (93-XX) 1 Mathematical logic and foundations (03-XX) 1 Category theory; homological algebra (18-XX) 1 Potential theory (31-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Classical thermodynamics, heat transfer (80-XX)