Measure-valued limits of interacting particle systems with k-nary interactions

Probability Theory and Related Fields

Volumn 126, Issue 3, 2003, Pages 364-394

  Kolokoltsov, Vassili N ^a  

^a NOTTINGHAM TRENT UNIVERSITY   (United Kingdom)

Author keywords

Duality Stochastic monotonicity; Heat kernel; Interacting particles; K nary interaction; Measure valued processes; One dimensional Feller processes with polynomially growing symbols

Indexed keywords

EID: 0041742505     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-003-0267-1     Document Type: Article

References (18)

1. [Al] Aldous, D.J.: Deterministic and stochastic models for coalescence (aaggregation and coagulation): a review of the mean-field theory for probabilists. Bernoulli 5(2), 3-48 (1999)
2. [An] Anderson, W.J.: Continuous-Time Markov Chains. Probability and its Applications. Springer Series in Statistics. Springer, 1991
3. [Be] Belavkin, V.P.: Quantum branching processes and nonlinear dynamics of multi-quantum systems. Dokl. Acad. Nauk SSSR 301(6), 1348-1352 (1988); Engl. Tansl. in Sov. Phys. Doki. 33(8), 581-582 (1988)
4. [Be] Belavkin, V.P.: Quantum branching processes and nonlinear dynamics of multi-quantum systems. Dokl. Acad. Nauk SSSR 301(6), 1348-1352 (1988); Engl. Tansl. in Sov. Phys. Doki. 33(8), 581-582 (1988)
5. [BK] Belavkin, V., Kolokoltsov, V.: On general kinetic equation for many particle systems with interaction, fragmentation and coagulation. Proc. R, Soc. Lond. A 459, 1-22 (2002)
6. [Br] Brémaud, P.: Markov Chains. Texts in Applied Mathematics, v. 31, Springer, 1999
7. [Dyn] Dynkin, E.B.: An Introduction to Branching Measure-Valued Processes. CRM Monograph Series, v. 6. AMS, Providence, Rhode Island, 1994
8. [EK] Ethier, S.N., Kurtz, T.G.: Markov Processes. Characterization and convergence. John Wiley Sons, 1986
9. [Fe] Feller, W.: The Parabolic Differential Equations and the Associated Semigroups of Transformations. Ann. of Math. 55, 468-519 (1952)
10. [Hi] Hille, E.: The Abstract Cauchy Problem and Cauchy's Problem for Parabolic Differential Equations. J. d'Analyse Math. 3, 81-196 (1953-1954)
11. [JS] Jacob, N., Schilling, R.L.: Lévy-Type Processes and Pseudodifferential Operators. In: O.E. Barndorff-Nielsen et al. (eds.). Lévy Processes, Theory and Applications. Birkhäuser 2001. pp. 139-168
12. [KFS] Kirstein, B.M., Franken, P., Stoyan, D.: Comparability and monotonicity of Markov processes. Theory of Probability and its Applications 22(1), 40-52 (1977)
13. [Kol1] Kolokoltsov, V.: Symmetric stable laws and stable-like jump-diffusions. Proc. London Math. Soc. 3(80), 725-768 (2000)
14. [Kol2] Kolokoltsov, V.: Semiclassical Analysis for Diffusions and Stochastic Processes. Springer Lecture Notes in Math. v., 1724, Spriger, 2000
15. [Kol3] Kolokoltsov, V.: Small diffusion and fast dying out asymptotics for superprocesses as non-Hamiltonian quasiclassics for evolution equations. Electronic Journal of Probability 6, paper 21 (2001)
16. [Kol4] Kolokoltsov, V.: Measure-valued limits of interacting particle systems with general k-nary interactions. II (in preparation)
17. [Man] Mandl, P.: Analytic Treatment of One-dimensional Markov Processes. Springer-Verlag, 1968
18. [N] Morris, J.: Cluster coagulation. Comm. Math. Phys. 209, 407-435 (2000)