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Filtered renewal processes with a two-sided impact function

Published online by Cambridge University Press:  14 July 2016

Per Kragh Andersen*
Affiliation:
Statistical Research Unit, Danish Medical and Social Science Research Councils

Abstract

An expression for the characteristic function of a stationary filtered renewal process with a two-sided impact function is derived, and formulae for the moments are obtained.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1979 

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References

Andersen, P. K., Andersen, S. and Lauritzen, S. L. (1977) The average noise from a Poisson stream of vehicles. J. Appl. Prob. 14, 817828.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications , vol. II, 2nd edn. Wiley, New York.Google Scholar
Johnson, D. R. and Saunders, E. G. (1968) The evaluation of noise from freely flowing road traffic. J. Sound and Vibration 7, 287309.Google Scholar
Karlin, S. (1955) On the renewal equation. Pacific J. Math. 5, 229257.Google Scholar
Marcus, A. H. (1973a) Traffic noise as a filtered Markov renewal process. J. Appl. Prob. 10, 377386.Google Scholar
Marcus, A. H. (1973b) A stochastic model of microscale air pollution from highway traffic. Technometrics 15, 353363.Google Scholar
Marcus, A. H. (1974) Environmental impacts of highway traffic as two-sided filtered Markov renewal processes. J. R. Statist. Soc. B 36, 426429.Google Scholar
Rozanov, Yu. A. (1967) Stationary Random Processes. Holden-Day, San Francisco.Google Scholar
Smith, W. K. (1973) Shot noise generated by a semi-Markov process. J. Appl. Prob. 10, 685690.Google Scholar
Smith, W. L. (1954) Asymptotic renewal functions. Proc. R. Soc. Edinburgh A 64, 948.Google Scholar
Smith, W. L. (1958) Renewal theory and its ramifications. J. R. Statist. Soc. B 20, 243302.Google Scholar
Takacs, L. (1954) On secondary processes generated by a Poisson process and their applications in physics. Acta Math. Acad. Sci. Hung. 5, 203236.Google Scholar
Takács, L. (1956) On secondary processes generated by recurrent processes. Acta Math. Acad. Sci. Hung. 7, 1729.Google Scholar
Weiss, G. H. (1970) On the noise generated by a stream of vehicles. Transportation Res. 4, 229233.Google Scholar