Abstract
Methods are developed for finding properties of the output of linear and nonlinear dynamic systems to random actions represented by Poisson white noise and filtered Poisson processes. The Poisson white noise can be viewed as a sequence of independent, identically distributed pulses arriving at random times. The filtered Poisson process is the output of a linear filter to Poisson white noise. Three methods are considered for finding output properties. If the input has infrequent or frequent pulses, output properties can be obtained from a Markov model or the assumption that the input is a Gaussian white noise, respectively. Otherwise, a method based on Itô's formula for semimartingales is used to find output properties. Examples are used to illustrate the proposed methods.
Similar content being viewed by others
References
Lin, Y. K., Probabilistic Theory of Structural Dynamics, Krieger, Huntington, New York, 1976.
Parzen, E., Stochastic Processes. Holden Day, San Francisco, California, 1944.
Roberts, J. B., 'The response of linear vibratory systems to random impulses', Journal of Sound and Vibration2(4) 1965, 375–390.
Grigoriu, M., Stochastic Calculus. Applications in Science and Engineering, Birkhäuser, Boston, Massachusetts, 2002.
Grigoriu, M., Applied Non-Gaussian Processes: Examples, Theory, Simulation, Linear Random Vibration, and MATLAB Solutions, Prentice Hall, Englewoods Cliffs, New Jersey, 1995.
Resnick, S. I., A Probability Path., Birkhäuser, Boston, Massachusetts, 1998.
Ariaratnam, S. T., 'Some illustrative examples of stochastic bifurcation', in Nonlinearity and Chaos in Engineering Dynamics, J. M. T. Thomson and S. R. Bishop (eds.), Wiley, New York, 1994, pp. 267–274.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Grigoriu, M. Dynamic Systems with Poisson White Noise. Nonlinear Dynamics 36, 255–266 (2004). https://doi.org/10.1023/B:NODY.0000045518.13177.3c
Issue Date:
DOI: https://doi.org/10.1023/B:NODY.0000045518.13177.3c