J. D. Biggins – Publications


Classified by topic; then in reverse chronological order.

Submitted:

Articles on the Branching Random Walk (BRW)

· Spreading speeds in reducible multi\-type branching random walk. To appear in Annals of Applied Probability arxiv.org/abs/1003.4716

· The Functional Equation of the Smoothing Transformation. To appear in Annals of Probability (with Gerold Almeyer and Matthais Meiners). arxiv.org/abs/0906.3133

· Multifractal spectra for random self-similar measures via branching processes. Adv. Appl. Probab 43 (2011) 1-39. (with Ben Hambly and Owen Jones)

· Branching out. In Probability and Mathematical Genetics: Papers in Honour of Sir John Kingman. Editors: N.H.~Bingham, C.M. Goldie; Cambridge University Press, 2010, 112--133. arxiv.org/abs/1003.4715

·  The smoothing transform: the boundary case. (with A.E. Kyprianou ). Electronic Journal In Probability (2005), 10, 609-631.

·  Convergence results in multitype, multivariate, branching random walk. (with A. Rahimzadeh Sani). Adv. Appl. Probab. (2005) 37(3)

·  Lindley-type equations in the branching random walk Stoc. Proc. Appl. (1998), 75, 105-133.

·  Seneta-Heyde norming in the branching random walk (with A.E.Kyprianou ). Ann. Probab. (1997) 25 337-360.

·  A note on the growth of random trees (with D.R. Grey). Statistics and Probability Letters (1997), 32, 339-342.

·  Branching random walk: Seneta-Heyde norming (with A.E.Kyprianou ). In Trees: Proceedings of a Workshop held in Versailles June 14-16, 1995, eds B. Chauvin, S. Cohen, A. Rouault. Birkhäuser, Basel. (1996), 31-50

·  How fast does a general branching random walk spread? In Classical and Modern Branching processes, (K.B. Athreya, P. Jagers, eds.). IMA Volumes in Mathematics and its Applications (1996) 84, 19-40. Springer-Verlag, New York.

·  The growth and spread of the general branching random walk Annals of Applied Probability, (1995) 5, 1008-1024.

·  Martingale convergence and large deviations in the branching random walk. Theory Probab. and Appl. (1992) 37, 301-306.

·  Uniform convergence of martingales in the branching random walk Ann. Probab. (1992), 20, 137-151.

·  Branching random walk with a barrier, (with B. Lubachevsky, A. Shwartz, A. Weiss) Ann. Appl. Probab. (1991) 1, 573-581.

·  Uniform convergence of martingales in the one-dimensional branching random walk. IMS lectures notes -- Monograph Series. Selected proceedings of the Sheffield Symposium on Applied Probability, 1989, Eds. I.V. Basawa and R.L. Taylor. (1991), 18, 159-173.

·  The central limit theorem for the supercritical branching random walk, and related results. Stoc. Proc. Appl. (1990), 34, 255-274.

·  Variants of the simple branching process. In Stochastic Modelling in Biology; relevant mathematical concepts and recent applications. Ed. P. Tautu. World Scientific, London. (1990), 250-266.

·  Limiting point processes in the branching random walk. Z. Wahrsch. verw. Geb. (1981), 55, 297-303.

·  Spatial spread in branching processes. Lecture Notes in Biomathematics, Biological Growth and Spread. (Eds. W. Jäger, H. Rost, P. Tautu). Springer. (1980), 38, 57-67.

·  Continuity of limit random variables in the branching random walk, (with D.R. Grey). Jnl. Appl. Probab. (1979), 16, 740-749.

·  Growth rates in the branching random walk. Z. Wahrsch. verw. Geb. (1979), 48, 17-34.

·  The asymptotic shape of the branching random walk. Adv. Appl. Probab. (1978), 10, 62-84.

·  Chernoff's Theorem in the branching random walk. Jnl. Appl. Probab. (1977), 14, 630-636.

·  Martingale convergence in the branching random walk. Jnl. Appl. Probab (1977), 14, 25-37.

·  The first and last birth problems for a multitype age-dependent branching process. Adv. Appl. Probab (1976), 8, 446-459.

Articles on Branching processes (but not just BRW)

·  Measure change in multitype branching (with A.E.Kyprianou ) Adv. Appl. Probab. (2004), 36, 544-581

·  Multi-type branching in varying environment (with H.Cohn. and O.Nerman. ) Stoc. Proc. Appl. (1999) 83, 357-400.

·  Large deviations in the supercritical branching process, (with N.H. Bingham). Adv. Appl. Probab. (1993) 25 757-772.

·  The supercritical Galton-Watson process in varying environments - Seneta-Heyde norming, (with J.C. D'Souza ). Stoc. Proc. Appl. (1993) 48 237-249.

·  Near-constancy of the Harris function in the simple branching process, (with S. Nadarajah). Stoc. Models. (1993) 9, 435-444

·  The Supercritical Galton-Watson process in varying environments, (with J.C. D'Souza ) Stoc. Proc. Appl. (1992) 42, 39-47.

·  The supercritical Galton-Watson process in varying environments, (with J.C. D'Souza ). Theory Probab. and Appl. (1992) 37, 206-207.

·  Near-constancy phenomena in branching processes, (with N.H. Bingham) Math. Proc. Camb. Phil. Soc. (1991), 110, 545-558.

·  Expected population size in the generation-dependent branching process, (with T. Götz). Jnl. Appl. Probab. (1987), 24, 304-314.

·  Some divisibility problems in branching processes, (with D.N. Shanbhag). Math. Proc. Camb. Phil. Soc. (1981), 90, 321-330.

Articles on other Applied Probability

·  Large deviations in randomly coloured random graphs. (with D.B. Penman).    Elect. Comm. in Probab. (2009), 14, 290-301.

·  The growth of iterates of multivariate generating functions.    Trans. Amer. Math. Soc. (2008), 360, 4305-4334.

·  Large deviations for mixtures.   Elect. Comm. in Probab. (2004), 9, 60-71.

·  Random walk conditioned to stay positive Jnl. Lond. Math. Soc.(2003), 67, 259-272

·  Formulae for mean restriction fragment lengths and related quantities, (with C. Cannings). Am. J. Hum. Genet. (1987), 41, 258-265

·  A note on repeated sequences in Markov Chains. Adv. Appl. Probab. (1987), 19, 739-742.

·  Markov renewal processes, counters and repeated sequences in Markov Chains, (with C. Cannings). Adv. Appl. Probab. (1987), 19, 521-545.

 

Articles on Statistical Methodology

·  A likelihood approach to scaling examination marks (with K.K. Yue) Austral. J. Statist. (1995) 37, 273-282.

·  Scaling and combining examination marks, (with K.K. Yue). Brit. J. Math. Statist. Psych. (1993) 46, 153-179.

·  Combining Examination Marks, (with R.M. Loynes, A.N. Walker). Brit. J. Math. Statist. Psych. (1986), 39, 150-167.

Articles on Applied Statistics

·  Non-transitivity of paternity in a bird. (with T.R.Birkhead, N.Chaline, T.Burke, T.Pizzari). Evolution to appear

·  Sperm competition mechanisms in birds: models and data. (with T.R.Birkhead) Behavioural Ecology (1998) 9 253-260.

·  Sperm precedence in the domestic fowl (with T.R. Birkhead, G.J. Wishart). Proc. R. Soc. B (1995) 261 285-292.

·  Reproductive synchrony and Extra-pair Copulation in Birds, (with T.R. Birkhead). Ethology (1987), 74, 320-334.

·  Breeding site characteristics and reproductive success in thick-billed murres, (with T.R. Birkhead, E. Greene, D.N. Nettleship). Can. J. Zool. (1985), 63, 1880-1884.

·  Factors affecting the peak expiratory flow rate in children, (with R.A. Primhak, J.N. Tsanakas, R.D.G. Milner, J.G. Karpouzas). Brit. J. Dis. Chest (1984), 78, 26-35.

·  Non-random intra-colony distribution of bridled guillemots, Uria aalge, (with T.R. Birkhead, D.N. Nettleship). J. Zool. Lond. (1980), 192, 9-16.

Abstracts and other short non-refereed contributions:

·  Contribution to the discussion of `Statistical and Decision Theoretic aspects of examination assessment' by S. French. Trab. de Estadística (1990), 5, 95-97.

·  Seconded vote of thanks at the RSS Symposium on Stochastic Networks. Jnl. Royal Statist. Soc. B (1985), 47, 417-418.

·  Large deviations and the branching random walk. Stoc. Proc. Appl. (1982), 12, 123

·  Spatial spread in branching processes. Adv. Appl. Probab. (1980), 12, 549

Unpublished research reports:

·  On repeated sequences in Markov chains (1986). Research Report 279/86.

·  Female risk and extra-pair copulation, (with T.R. Birkhead) (1986). Research Report 282/86.

·  Extended Perron-Frobenius results (with A. Rahimzadeh Sani) . Research Report 539/04


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