Eternal solutions to Smoluchowski's coagulation equation with additive kernel and their probabilistic interpretations

Annals of Applied Probability

Volumn 12, Issue 2, 2002, Pages 547-564

  Bertoin, Jean ^a  

^a INSTITUT UNIVERSITAIRE DE FRANCE   (France)

Author keywords

Additive coalescence; Levy process with no positive jumps; Smoluchowski's coagulation equation

Indexed keywords

EID: 0036330936     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1026915615     Document Type: Article

References (26)

1. ALDOUS, D. J. (1999). Deterministic and stochastic models for coalescence (aggregation, coagulation): a review of the mean-field theory for probabilists. Bernoulli 5 3-48.
2. ALDOUS, D. J. and PITMAN, J. (1998). The standard additive coalescent. Ann. Probab. 26 1703-1726.
3. ALDOUS, D. J. and PITMAN, J. (2000). Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent. Probab. Theory Related Fields 118 455-482.
4. BERTOIN, J. (1996). Levy Processes. Cambridge University Press.
5. BERTOIN, J. (1999). Subordinates: examples and applications. École d'été de Probabilités de St-Flour XXVII. Lecture Notes in Math, 1717 1-91. Springer, Berlin.
6. BERTOIN, J. (2000). A fragmentation process connected to Brownian motion. Probab. Theory Related Fields 117 289-301.
7. BERTOIN, J. (2001). Eternal additive coalescents and certain bridges with exchangeable increments. Ann. Probab. 29 344-360.
8. CAMARRI, M. and PITMAN, J. (2000). Limit distributions and random trees derived from the birthday problem with unequal probabilities. Electron. J. Probab. 5.
9. CHASSAING, P. and LOUCHARD, G. (2001). Phase transition for parking blocks, Brownian excursions and coalescence. Random Structures Algorithms. To appear.
10. DEACONU, M., FOURNIER, N. and TANRÉ, E. (2001). A pure jump Markov process associated with Smoluchowski's coagulation equation. Ann. Probab. To appear.
11. DEACONU, M., FOURNIER, N. and TANRÉ, E. (2001). Study of a stochastic particle system associated with the Smoluchowski coagulation equation. Preprint.
12. DEACONU, M. and TANRÉ, E. (2000). Smoluchovski's coagulation equation: Probabilistic interpretation of solutions for constant, additive and multiplicative kernels. Ann. Scuola Norm. Sup. Pisa 29 549-580.
13. DRAKE, R. L. (1972). A general mathematical survey of the coagulation equation. In Topics in Current Aerosol Research, Part 2 (G. M. Hidy and J. R. Brock, eds.) 201-376. Pergamon Press, Oxford.
14. EVANS, S. N. and PITMAN, J. (1998). Construction of Markovian coalescents. Ann. Inst. H. Poincaré Probab. Statist. 34 339-383.
15. GOLOVIN, A. M. (1963). The solution of the coagulation equation for cloud droplets in a rising air current. Izv. Geophys. Ser. 5 482-487.
16. KINGMAN, J. F. C. (1975). Random discrete distributions. J. Roy. Statist. Soc. Ser. B 37 1-22.
17. LAMPERTI, J. (1967). The limit of a sequence of branching processes. Z. Wahrsch. Verw. Gebiete 7 271-288.
18. LAMPERTI, J. (1967). Continuous-state branching processes. Bull. Amer. Math. Soc. 73 382-386.
19. LUSHNIKOV, A. A. (1978). Certain new aspects of the coagulation theory. Izv. Atmos. Ocean Phys. 14 738-743.
20. MARCUS, A. H. (1968). Stochastic coalescence. Technometrics 10 133-143.
21. McLEOD, J. B. (1964), On the scalar transport equation. Proc. London Math. Soc. (3) 14 445-458.
22. MIERMONT, G. (2001). Ordered additive coalescent and fragmentations associated to Levy processes with no positive jumps. Electron. J. Probab. 6.
23. NORRIS, J. R. (1999). Smoluchowski's coagulation equation: Uniqueness, non-uniqueness and hydrodynamic limit for the stochastic coalescent. Ann. Appl. Probab. 9 78-109.
24. SATO, K.-I. (1999). Levy Processes and Infinitely Divisible Distributions. Cambridge Univ. Press.
25. SCHWEINSBERG, J. (2001). Applications of the continuous-time ballot theorem to Brownian motion and related processes. Stochastic Process. Appl. 95 151-176.
26. SHETH, R. K. and PITMAN, J. (1997). Coagulation and branching process models of gravitational clustering. Monthly Notices of the Royal Astronomy Society 289 66-80.