Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-22T04:25:34.538Z Has data issue: false hasContentIssue false
  • English
  • Français

A stochastic explosive reaction system with sampling

Published online by Cambridge University Press:  14 July 2016

Donald A. Dawson  and
Klaus Fleischmann
Donald A. Dawson*
Affiliation:
Carleton University
Klaus Fleischmann*
Affiliation:
Academy of Sciences of the GDR
*
∗Postal address: Department of Mathematics and Statistics, Carleton University, Ottawa, Canada K1S 5B6.
∗∗Postal address: Karl Weierstrass Institute of Mathematics, Academy of Sciences of the GDR, Box 1304, Berlin, DDR-1086, GDR.
Get access Rights & Permissions [Opens in a new window]

Abstract

Large stochastic systems of marked particles are considered. These ‘populations' grow according to pairwise mutually catalytic reactions and in addition particles may exchange their type (mark) by a sampling procedure. We are interested in the explosive behavior of the model and its high density properties (law of large numbers).

Keywords

CHEMICAL REACTIONEXPLOSIVE SYSTEMSHIGH DENSITY LIMITREACTION KINETICS
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 1 , March 1989 , pp. 9 - 22
Copyright
Copyright © Applied Probability Trust 1989 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Athreya, K. B. (1969) On a characteristic property of Pólya's urn. Stud. Sci. Math. Hung. 4, 31–35.Google Scholar
[2] Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
[3] Dawson, D. A. and Hochberg, K. J. (1982) Wandering random measures in the Fleming–Viot model. Ann. Prob. 10, 554–580.CrossRefGoogle Scholar
[4] Eigen, M. and Schuster, P. (1979) The Hypercycle. Springer-Verlag.CrossRefGoogle Scholar
[5] Fife, P. C. (1979) Mathematical Aspects of Reacting and Diffusing Systems. Lecture Notes in Biomathematics 28, Springer-Verlag, Berlin.Google Scholar
[6] Gihman, I. I. and Skorohod, A. V. (1980) The Theory of Stochastic Processes I. Springer-Verlag, Berlin.Google Scholar
[7] Johnson, N. L. and Kotz, S. (1977) Urn Models and Their Application. Wiley, New York.Google Scholar
[8] Kurtz, T. G. (1970) Solutions of ordinary differential equations as limit of pure jump Markov processes. J. Appl. Prob. 7, 49–58.Google Scholar