Skip to main content Accessibility help

The propagation of chaos of multitype mean field interacting particle systems

  • Shui Feng (a1)


A result for the propagation of chaos is obtained for a class of pure jump particle systems of two species with mean field interaction. This result leads to the corresponding result for particle systems with one species and the argument used is valid for particle systems with more than two species. The model is motivated by the study of the phenomenon of self-organization in biology, chemistry and physics, and the technical difficulty is the unboundedness of the jump rates.


Corresponding author

Postal address: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada.


Hide All

Research supported by the SERB grant at McMaster University and by the Natural Sciences and Engineering Research Council of Canada.



Hide All
[1] Chen, M. F. (1992) From Markov Chains to Non-Equilibrium Particle System. World Scientific, Singapore.
[2] Dawson, D. A. (1983) Critical dynamics and fluctuations for a mean-field model of cooperative behaviour. J. Statist. Phys. 31, 2985.
[3] Dawson, D. A. and Zheng, X. (1991) Law of large numbers and a central limit theorem for unbounded jump mean-field models. Adv. Appl. Math. 12, 293326.
[4] Feng, S. (1995) Nonlinear master equation of multitype particle systems. Stoch. Proc. Appl. to appear.
[5] Feng, S. and Zheng, X. (1992) Solutions of a class of nonlinear master equations. Stoch. Proc. Appl. 43, 6584.
[6] Ferland, R. and Giroux, G. (1992) An unbounded mean field intensity model: propagation of the convergence of the empirical laws and compactness of the fluctuations. Preprint.
[7] Lotka, A. J. (1920) Undamped oscillations derived from the law of mass action. J. Amer. Chem. Soc. 42, 15951599.
[8] Scheutzow, M. (1985) Some examples of nonlinear diffusions having a time-periodic law. Ann. Prob. 13, 379384.
[9] Scheutzow, M. (1986) Periodic behavior of the stochastic Brusselator in the mean-field limit. Prob. Theory Rel. Fields 72, 425462.
[10] Shiga, T. and Tanaka, H. (1985) Central limit theorem for a system of Markovian particles with mean-field interactions. Z. Wahrscheinlichkeitsth. 69, 439459.
[11] Sznitman, S. A. (1984) Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated. J. Funct. Anal. 56, 311336.
[12] Sznitman, S. A. (1991) Topics in propagation of chaos. In Lecture Notes in Mathematics 1464. Springer, Berlin, pp. 167251.
[13] Tanaka, H. (1984) Limit theorems for certain diffusion processes with interactions. In Taniguchi Symp., Katata. Kinokuniya, Tokyo, pp. 469488.
[14] Volterra, V. (1926) Variazioni fluttuazioni del numero d'individui in specie animali conviventi. Mem. Acad. Lincei. 2, 31113.
[15] Zheng, J. L. and Zheng, X. G. (1987) A martingale approach to q-process. Chinese Kexue Tongbao 22, 14571459.


MSC classification

The propagation of chaos of multitype mean field interacting particle systems

  • Shui Feng (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed