References: |
[Al] D.J. Aldous. Deterministic and stochastic models for coalescence (aggregation and coagulation): a review of the mean-field theory for probabilists. Bernoulli 5:2 (1999), 3-48. [Am] H. Amann. Coagulation-Fragmentation processes. Arch. Rational Mech. Anal. 151 (2000), 339-366. [BC] J.M. Ball, J. Carr. The discrete coagulation-fragmentation equations: existence, uniqueness and density conservation. J. Stat. Phys. 61 (1990), 203-234. [Be] V.P. Belavkin. Quantum branching processes and nonlinear dynamics of multi- quantum systems. Dokl. Acad. Nauk SSSR 301:6 (1988), 1348-1352. Engl. Tansl. in Sov. Phys. Dokl. 33:8 (1988), 581-582. [BK] V. Belavkin, V. Kolokoltsov. On general kinetic equation for many particle systems with interaction, fragmentation and coagulation. Proc. R. Soc. Lond. A 459 (2002), 1-22. [BW] Ph. Benian, D. Wrzosek. On infinite system of reaction-diffusion equations. Adv. Math. Sci. Appl. 7 (1997), 349-364. [Br1] J. Bertoin. Homogeneous fragmentation processes. Prob. Theory Relat. Fields 121 (2001), 301-318. [Br2] J. Bertoin. Self-similar fragmentations. Ann. Inst. H. Poincare Probab. Stat. 38 (2002), 319-340. [BL] J. Bertoin, J.-F. LeGall. Stochastic flows associated to coalescent processes. Preprint 2002 Available via http://felix.proba.jussieu.fr/mathdoc/preprints/ [CC] J. Carr, F. da Costa. Instantaneous gelation in coagulation dynamics. Z. Angew. Math. Phys. 43 (1992), 974-983. [CP] J.F. Collet, F. Poupaud. Existence of solutions to coagulation-fragmentation systems with diffusion. Transport Theory Statist. Phys. 25 (1996), 503-513. [Da] D. Dawson. Measure-Valued Markov Processes. Hennequin P.L. (ed.) Ecole d'Ete de probabilit¶es de Saint-Flour XXI-1991. Springer Lect. Notes Math. 1541 (1993), 1-260. [DKW] S.C. Davies, J.R. King and J.A. Wattis. The Smoluchovski coagulation equations with continuous injection. J. Phys. A: Math. Gen. 32 (1999), 7745-7763. [Du] P.B. Dubovski. A "triangle" of interconnected coagulation models. J. Phys. A: Math.Gen. 32 (1999), 781-793. [Dy] E. Dynkin. An Introduction to Branching Measure-Valued Processes. CRM monograph series 6, AMS, Providence RI, 1994. [EK] S.N. Ethier, T.G. Kurtz. Markov Processes. Characterization and convergence. John Wiley Sons 1986. [Ja] N. Jacob. Pseudo-differential operators and Markov processes. Vol. II: Generators and their potential theory. London: Imperial College Press, 2002. [Je] I. Jeon. Existence of Gelling Solutions for Coagulation-Fragmentation Equations. Comm. Math. Phys. 194 (1998), 541-567. [Ko1] V. Kolokoltsov. Measure-valued limits of interacting particle systems with k-nary interactions I. One-dimensional limits. Probab. Theory Relat. Fields 126 (2003), 364-394. [Ko2] V. Kolokoltsov. Measure-valued limits of interacting particle systems with k-nary interactions II. Preprint (2002). To appear in Stochastics and Stochastics Reports. [Ko3] V. Kolokoltsov. On Extensions of Mollified Boltzmann and Smoluchovski Equations to Particle Systems with a k-nary Interaction. Russian Journal Math. Phys. 10:3 (2003), 268-295. [Ko4] V. Kolokoltsov. Symmetric stable laws and stable-like jump-diffusions. Proc. London Math. Soc. 3:80 (2000), 725-768. [Ko5] V. Kolokoltsov. On Markov processes with decomposable pseudo-differential generators. Preprint (2002). To appear in Stochastics and Stochastics Reports. [KK] M. Kostoglou, A.J. Karabelas. A study of nonlinear breakage equation: Analytical and asymptotic solutions. J. Phys. A: Math.Gen. 33 (2000), 1221-1232. [LLW] M. Lachowicz, Ph. Laurencot, D. Wrzosek. On the Oort-Hulst-Savronov coagulation equation and its relation to the Smoluchowski equation. SIAM J. Math. Anal. 34 (2003), 1399-1421. [LM] Ph. Laurencot, S. Mischler. The Continuous Coagulation-Fragmentation Equations with Diffusion. Arch. Rational Mech. Anal. 162 (2002), 45-99. [LW] P. Laurencot, D. Wrzosek. The Discrete Coagulation Equations with Collisional Breakage. J. Stat. Phys. 104, 1/2 (2001), 193-220. [MS] M. MÄohle, S. Sagitov. A classification of coalescent processes for haploid exchangeable population models. Ann. Prob. 29 (2001), 1547-1562. [No1] J. Norris. Smoluchovski's Coagulation Equation: Uniqueness, Nonuniqueness and a Hydrodynamic Limit for the Stochastic Coalescent. The Annals of Applied Probability 9:1 (1999), 78-109. [No2] J. Norris. Cluster Coagulation. Comm. Math. Phys. 209 (2000), 407-435. [Ok] A. Okubo. Dynamical aspects of animal grouping: swarms, schools, flocks and herds. Adv. Biophys 22 (1986), 1-94. [Pi] J.Pitman. Coalescents with multiple collisions. Ann. Prob. 27 (1999), 1870-1902. [Sa] V.S. Safronov. Evolution of the Pre-Planetary Cloud and the Formation of the Earth and Planets. Moscow, Nauka, 1969 (in Russian). Engl. transl.: Israel Program for Scientific Translations, Jerusalem, 1972. [Sc] J. Schweinsberg. Coalescents with simultaneous multiple collisions. Electr. J. Prob. 5 (2000), 1-50. [Sr] R.C. Srivastava. A simple model of particle coalescence and breaup. J. Atmos. Sci. 39 (1982), 1317-1322. [Sz] A. Sznitman. Topics in Propagation of Chaos. In: Ecole d'Ete de Probabilites de Saint-Flour XIX-1989. Springer Lecture Notes Math. 1464 (1991), 167-255. [Wi] D. Wilkins. A geometrical interpretation of the coagulation equation. J. Phys. A: Math. Gen. 15 (1982), 1175-1178. [Wr] D. Wrzosek. Mass-conservation solutions to the discrete coagulation-fragmentation model with diffusion. Nonlinear Anal. 49 (2002), 297-314. |