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Solutions of ordinary differential equations as limits of pure jump markov processes

Published online by Cambridge University Press:  14 July 2016

Thomas G. Kurtz
Thomas G. Kurtz*
Affiliation:
University of Wisconsin
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Extract

In a great variety of fields, e.g., biology, epidemic theory, physics, and chemistry, ordinary differential equations are used to give continuous deterministic models for dynamic processes which are actually discrete and random in their development. Perhaps the simplest example is the differential equation used to describe a number of processes including radioactive decay and population growth.

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 1 , April 1970 , pp. 49 - 58
Copyright
Copyright © Applied Probability Trust 

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References

[1] Dynkin, E. B. (1965) Markov Processes I. Academic Press, New York, and Springer-Verlag, Berlin-Göttingen-Heidelberg.Google Scholar
[2] Kemeny, J. G. and Snell, J. L. (1962) Mathematical Models in the Social Sciences. Ginn and Company, Boston.Google Scholar
[3] Kurtz, T. G. (1969) Extensions of Trotter's operator semigroup approximation theorems. J. Functional Anal. 3, 111–132.CrossRefGoogle Scholar