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The stationary moments of Poisson-driven non-linear dynamical systems

Published online by Cambridge University Press:  14 July 2016

Charles E. Smith  and
Loren Cobb
Charles E. Smith*
Affiliation:
Medical University of South Carolina
Loren Cobb*
Affiliation:
Medical University of South Carolina
*
∗Postal address: Department of Biometry, College of Medicine, Medical University of South Carolina, Charleston, SC 29425, U.S.A.
∗Postal address: Department of Biometry, College of Medicine, Medical University of South Carolina, Charleston, SC 29425, U.S.A.
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Abstract

Moment recursion relations have previously been derived for the stationary probability density functions of continuous-time stochastic systems with Wiener (white noise) input. These results are extended in this paper to the case of Poisson (shot noise) input. The non-linear dynamical systems are expressed, in general, as stochastic differential equations, with an independent increment input. The transition probability density function evolves according to the appropriate Kolmogorov equation. Moments of the stationary density are obtained from the Fourier transform of the stationary density. The moment relations can be used to estimate the parameters of linear and non-linear stochastic systems from empirical moments, given either Wiener or Poisson input.

Keywords

MOMENT RECURSION RELATIONSNON-LINEAR STOCHASTIC DIFFERENTIAL EQUATIONSFILTERED POINT PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 702 - 706
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

This research was supported by the National Science Foundation, Grant #80–11451, and the South Carolina State Appropriation for Biomedical Research.

References

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