Hostname: page-component-74656f9884-g96k6 Total loading time: 0 Render date: 2026-11-10T23:44:32.848Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximate solutions for coupled moment equations

Published online by Cambridge University Press:  17 February 2009

Graham Winley  and
Keith Tognetti
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In studying the coupled differential equations for the moments of a stochastic process it is often found that the equation for the j th moment involves higher moments. The usual methods of “decoupling” such a system of equations to obtain estimates of the moments are surveyed and shown generally to result in a system of nonlinear simultaneous differential equations which may be readily solved by numerical methods.

Often, estimates of the first and second moments are the main concern. In this case, two further assumptions reported in the literature can be used to simplify the system and avoid the expense of solving the nonlinear equations. These two techniques are evaluated and compared with a new technique. Two processes are analysed, one representing a chemical reaction and the other population growth.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 24 , Issue 1 , July 1982 , pp. 86 - 97
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Bailey, N. T. J., The elements of stochastic processes with applications to the natural sciences (Wiley, New York, 1964).Google Scholar
[2]Goel, N. S. and Richter-Dyn, N., Stochastic models in biology (Academic Press, New York, 1974).Google Scholar
[3]Kendall, D. G., “Stochastic processes and population growth” (Symposium on Stochastic Processes), J. Roy. Stat. Soc. B11 (1949), 230–264.Google Scholar
[4]McQuarrie, D. A., Stochastic approach to chemical kinetics (Methuen, London, 1968).Google Scholar
[5]Pielou, E. C., An introduction to mathematical ecology (Wiley, New York, 1969).Google Scholar
[6]Tognetti, K. and Winley, G., “Stochastic growth models with logistic mean population”, J. Theor. Biol. 82 (1980), 167–169.CrossRefGoogle ScholarPubMed
[7]Wang, Y. K., “Noise effects and transient behaviour for a laser”, Ph.D. Thesis, Yale University, New Haven, Connecticut, 1971.Google Scholar