Construction of markovian coalescents
Annales de l'I.H.P. Probabilités et statistiques (1998)
- Volume: 34, Issue: 3, page 339-383
- ISSN: 0246-0203
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topEvans, Steven N., and Pitman, Jim. "Construction of markovian coalescents." Annales de l'I.H.P. Probabilités et statistiques 34.3 (1998): 339-383. <http://eudml.org/doc/77606>.
@article{Evans1998,
author = {Evans, Steven N., Pitman, Jim},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Feller process; additive coalescent; random graph process; stable subordinator},
language = {eng},
number = {3},
pages = {339-383},
publisher = {Gauthier-Villars},
title = {Construction of markovian coalescents},
url = {http://eudml.org/doc/77606},
volume = {34},
year = {1998},
}
TY - JOUR
AU - Evans, Steven N.
AU - Pitman, Jim
TI - Construction of markovian coalescents
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1998
PB - Gauthier-Villars
VL - 34
IS - 3
SP - 339
EP - 383
LA - eng
KW - Feller process; additive coalescent; random graph process; stable subordinator
UR - http://eudml.org/doc/77606
ER -
References
top- [1] D. Aldous. Brownian excursions, critical random graphs and the multiplicative coalescent. Ann. Probab., Vol. 25, 1997, pp. 812-854. Zbl0877.60010MR1434128
- [2] D. Aldous and J. Pitman. Brownian bridge asymptotics for random mappings. Random Structures and Algorithms, Vol. 5, 1994, pp. 487-512. Zbl0811.60057MR1293075
- [3] D. Aldous and J. Pitman. The entrance boundary of the additive coalescent. Paper in preparation, 1997.
- [4] D.J. Aldous. Exchangeability and related topics. In P.L. Hennequin, editor, École d'Été de Probabilités de Saint-FlourXII, Springer Lecture Notes in Mathematics, Vol. 1117. Springer-Verlag, 1985. Zbl0562.60042MR883646
- [5] D.J. Aldous. The continuum random tree III. Ann. Probab., Vol. 21, 1993, pp. 248-289. Zbl0791.60009MR1207226
- [6] D.J. Aldous. Deterministic and stochastic models for coalescence: a review of the mean-field theory for probabilists. To appear in Bernoulli. Available via homepage http://www.stat.berkeley.edu/users/aldous, 1997. Zbl0930.60096MR1673235
- [7] D.J. Aldous and V. Limic. The entrance boundary of the multiplicative coalescent. Unpublished. Available via homepage http://www.stat.berkeley.edu/users/aldous, 1997.
- [8] D.J. Aldous and J. Pitman. The standard additive coalescent. Technical Report 489, Dept. Statistics, U.C. Berkeley, 1997. Available via http://www.stat.berkeley.edu/users/pitman. Zbl0936.60064
- [9] A. Benveniste and J. Jacod. Systèmes de Levy des processus deMarkov. Invent. Math., Vol. 21, 1973, pp. 183-198. Zbl0265.60074MR343375
- [10] R.M. Blumenthal and R.K. Getoor. Markov Processes and Potential Theory. Academic Press, New York, 1968. Zbl0169.49204MR264757
- [11] E. Bolthausen and A.-S. Sznitman. On Ruelle's probability cascades and an abstract cavity method. To appear in Comm. Math. Phys., 1998. Zbl0927.60071MR1652734
- [12] A. Broder. Generating random spanning trees. In Proc. 30'th IEEESymp. Found. Comp. Sci., 1989, pp. 442-447.
- [13] A. Cayley. A theorem on trees. Quarterly Journal of Pure and Applied Mathematics, 23:376-378, 1889. (Also in The Collected Mathematical Papers of Arthur CAYLEY. Vol. XIII, pp. 26-28, Cambridge University Press, 1897). Zbl21.0687.01JFM21.0687.01
- [14] D.A. Dawson. Measure-valued Markov processes. In École d'Été de Probabilités de Saint-Flour, 1991, Springer Lecture Notes in Mathematics, Vol. 1117, 1994. Zbl0799.60080MR1242575
- [15] P. Donnelly and P. Joyce. Continuity and weak convergence of ranked and size-biased permutations on the infinite simplex. Stochastic Processes and their Applications, Vol. 31, 1989, pp. 89-103. Zbl0694.60009MR996613
- [16] P. Donnelly and S. Simons. On the stochastic approach to cluster size distribution during particle coagulation I: Asymptotic expansion in the deterministic limit. J. Phys. A: Math. Gen., Vol. 26, 1993, pp. 2755-2767. Zbl0788.60127MR1236145
- [17] S.N. Ethier and T.G. Kurtz. Fleming-Viot processes in population genetics. SIAM Journal on Control and Optimization, Vol. 31, 1993, pp. 345-386. Zbl0774.60045MR1205982
- [18] S.N. Evans. Infinitely-many-species Lotka-Volterra equations arising from systems of coalescing masses. Technical Report 478, Dept. Statistics, U.C. Berkeley, 1997. To appear in J. London Math. Soc.. Available via http://www.stat.berkeley.edu/tech-reports. Zbl0940.35051MR1721823
- [19] S.N. Evans and J. Pitman. Stationary Markov processes related to stable Ornstein-Uhlenbeck processes and the additive coalescent. Technical Report 488, Dept. Statistics, U.C. Berkeley, 1997. Available via http://www.stat.berkeley.edu/users/pitman. Zbl0934.60046MR1649003
- [20] E.M. Hendriks, J.L. Spouge, M. Eibl, and M. Shreckenberg. Exact solutions for random coagulation processes.Z. Phys. B - Condensed Matter, Vol. 58, 1985, pp. 219-227.
- [21] N. Ikeda and S. Watanabe. Stochastic Differential Equations andDiffusion Processes. North Holland/Kodansha, 1989. 2nd edition. Zbl0684.60040MR1011252
- [22] J.F.C. Kingman. Random discrete distributions.J. Roy. Statist. Soc. B, Vol. 37, 1975, pp. 1-22 Zbl0331.62019MR368264
- [23] J.F.C. Kingman. The representation of partition structures.J. London Math. Soc., Vol. 18, 1978, pp. 374-380. Zbl0415.92009MR509954
- [24] J.F.C. Kingman. The coalescent. Stochastic Processes and their Applications, Vol. 13, 1982, pp. 235-248. Zbl0491.60076MR671034
- [25] J.F.C. Kingman. On the genealogy of large populations. In J. Gani and E.J. Hannan, editors, Essays in Statistical Science, volume 19A of J.A.P. Special vol., pp. 27-43. Applied Probability Trust, 1982. Zbl0516.92011MR633178
- [26] C. Lacey and S. Cole. Merger rates in hierarchical models of galaxy formation. Mon. Not. R. Astron. Soc., Vol. 262, 1993, pp. 627-649.
- [27] A.A. Lushnikov. Coagulation in finite systems.J. Colloid and Interface Science, Vol. 65, 1978, 276-285.
- [28] R. Lyons and Y. Peres. Probability on trees and networks. Book in preparation, available at http://www.ma.huji.ac.il/lyons/prbtree.html, 1996.
- [29] A.H. Marcus. Stochastic coalescence. Technometrics, Vol. 10, 1968, pp. 133-143. MR223151
- [30] M. Perman. Order statistics for jumps of normalized subordinators. Stoch. Proc. Appl., Vol. 46, 1993, pp. 267-281. Zbl0777.60070MR1226412
- [31] M. Perman, J. Pitman, and M. Yor. Size-biased sampling of Poisson point processes and excursions. Probab. Th. Rel. Fields, Vol. 92, 1992, pp. 21-39. Zbl0741.60037MR1156448
- [32] J. Pitman. Exchangeable and partially exchangeable random partitions. Probab. Th. Rel. Fields, Vol. 102, 1995, pp. 145-158. Zbl0821.60047MR1337249
- [33] J. Pitman. Coalescent random forests. Technical Report 457, Dept. Statistics, U.C. Berkeley, 1996. Available via http://www.stat.berkeley.edu/users/pitman. Zbl0918.05042
- [34] J. Pitman. Random discrete distributions invariant under size-biased permutation. Adv. Appl. Prob., Vol. 28, 1996, pp. 525-539. Zbl0853.62018MR1387889
- [35] J. Pitman. Abel-Cayley-Hurwitz multinomial expansions associated with random mappings, forests and subsets. Technical Report 498, Dept. Statistics, U.C. Berkeley, 1997. Available via http://www.stat.berkeley.edu/users/pitman. Zbl0990.05071
- [36] J. Pitman. Coalescents with multiple collisions. Technical Report 495, Dept. Statistics, U.C. Berkeley, 1997. Available via http://www.stat.berkeley.edu/users/pitman. Zbl0963.60079
- [37] J. Pitman and M. Yor. The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Probab., Vol. 25, 1997, pp. 855-900. Zbl0880.60076MR1434129
- [38] A. Rényi. On the enumeration of trees. In R. Guy, H. Hanani, N. Sauer, and J. Schonheim, editors, Combinatorial Structures and their Applications, pages 355-360. Gordon and Breach, New York, 1970. Zbl0247.05102MR263708
- [39] R.K. Sheth. Merging and hierarchical clustering from an initially Poisson distribution. Mon. Not. R. Astron. Soc., Vol. 276, 1995, pp. 796-824.
- [40] R.K. Sheth and J. Pitman. Coagulation and branching process models of gravitational clustering. Mon. Not. R. Astron. Soc., Vol. 289, 1997, pp. 66-80.
- [41] R. Stanley. Enumerative combinatorics, vol. 2. Book in preparation, to be published byCambridge University Press, 1996. MR1676282
- [42] H. Tanaka and K. Nakazawa. Stochastic coagulation equation and validity of the statistical coagulation equation.J. Geomag. Geoelectr., Vol. 45, 1993, pp. 361-381.
- [43] H. Tanaka and K. Nakazawa. Validity of the stochastic coagulation equation and runaway growth of protoplanets. Icarus, Vol. 107, 1994, pp. 404-412.
- [44] H.M. Taylor and S. Karlin.An Introduction to Stochastic Modeling (revised ed.). Academic Press, Boston, 1994. Zbl0796.60001MR1242559
- [45] P.G.J. van Dongen. Fluctuations in coagulating systems II. J. Statist. Phys., Vol. 49, 1987, pp. 927-975. MR935481
- [46] P.G.J. van Dongen and M.H. Ernst. Fluctuations in coagulating systems. J. Statist. Phys., Vol. 49, 1987, pp. 879-926. MR935480
- [47] M. von Smoluchowski. Drei Vorträge über Diffusion, Brownsche Bewegung und Koagulation von Kolloidteilchen. Physik. Z., Vol. 17, 1916, pp. 557-585.
Citations in EuDML Documents
top- Jean Bertoin, Self-similar fragmentations
- Madalina Deaconu, Etienne Tanré, Smoluchowski's coagulation equation : probabilistic interpretation of solutions for constant, additive and multiplicative kernels
- Julien Berestycki, Ranked fragmentations
- Julien Berestycki, Ranked Fragmentations
- Anne-Laure Basdevant, On the equivalence of some eternal additive coalescents
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