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Shot noise generated by a semi-Markov process

Published online by Cambridge University Press:  14 July 2016

Woollcott Smith
Woollcott Smith*
Affiliation:
University of North Carolina at Chapel Hill
*
*Now at Woods Hole Oceanographic Institution, Woods Hole, Mass.
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Abstract

In this note a model for shot noise generated by a semi-Markov process is developed. The moments of the shot noise process are found, and some applications of this model are briefly indicated.

Keywords

SEMI-MARKOVSHOT NOISEINFINITELY MANY SERVER QUEUENEURAL SPIKE TRAINS
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 3 , September 1973 , pp. 685 - 690
Copyright
Copyright © Applied Probability Trust 1973 

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Footnotes

Research partially supported by the National Science Foundation under Grant No. GU-2059 and by the Air Force Office of Scientific Research under Contract No. AFOSR-68-1415.

References

Coleman, R. and Gastwirth, J. L. (1969) Some models for interaction of renewal processes related to neuron firing. J. Appl. Prob. 6, 38–58.10.2307/3212275Google Scholar
Gerstein, C. L. and Mandelbrot, B. (1964) Random walk models for spike activity of a simple neuron. Biophys. J. 4, 41–68.10.1016/S0006-3495(64)86768-0Google Scholar
Gilbert, E. N. and Pollak, H. C. (1960) Amplitude distribution of noise shot. Bell. Syst. Tech. J. 39, 333–350.10.1002/j.1538-7305.1960.tb01603.xGoogle Scholar
Marcus, A. H. (1971) Stochastic models of some environmental impacts of highway traffic. I: A two-sided filtered Markov renewal process. The Johns Hopkins University Technical Report No. 156.Google Scholar
Pyke, R. (1961) Markov renewal processes with finitely many states. Ann. Math. Statist. 32, 1243–1259.10.1214/aoms/1177704864Google Scholar
Perkel, G. L., Gerstein, G. L. and Moore, G. P. (1967) Neural spike trains and stochastic point processes, I. The single spike train. Biophys. J. 7, 391–418.10.1016/S0006-3495(67)86596-2Google Scholar
Smith, W. (1971) A general shot noise model applied to neural spike trains. Proceedings of the Third Annual Southeastern Symposium on System Theory, Vol. 2 (April 5–6, 1971).Google Scholar
Stevens, C. F. (1966) Neurophysiology: A Primer. John Wiley, New York.Google Scholar
Srinivasan, S. K. and Rajamannar, G. (1970) Counter models and dependent renewal point processes related to neural firing. Math. Biosci. 7, 27–39.10.1016/0025-5564(70)90040-4Google Scholar
Takács, L. (1956) On secondary stochastic processes generated by recurrent processes. Acta Math. Acad. Sci. Hung. 7, 17–29.10.1007/BF02022961Google Scholar
Takács, L. (1958) On a coincidence problem in telephone traffic. Acta Math. Acad. Sci. Hung. 6, 363–380.10.1007/BF02024395Google Scholar
Takács, L. (1960) Stochastic Processes. Methuen, London.Google Scholar
Ten Hoopen, M. and Reuven, H. A. (1968) Recurrent point processes with dependent interference with reference to neural spike trains. Math. Biosci. 2, 1–10.10.1016/0025-5564(68)90002-3Google Scholar
Ten Hoopen, M. and Reuven, H. A. (1965) Selective interaction of two recurrent processes. J. Appl. Prob. 2, 286–292.10.2307/3212195Google Scholar
Tricomi, F. (1957) Integral Equations. Wiley, New York.Google Scholar