Advertisement

Filtered Poisson-Processes

  • Donald L. Snyder
  • Michael I. Miller
Part of the Springer Texts in Electrical Engineering book series (STELE)

Abstract

There are numerous physical phenomena that can be modeled as a response to the points of a marked point process. The simplest models occur when the response can be expressed as a superposition of separate responses to each marked point. These models are developed in Sec. 5.2. Later, in Sec. 5.3, we remove the superposition requirement but impose the additional structure of Markov processes.

Keywords

Poisson Process Point Process Shot Noise Occurrence Time Point Response 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T. M. Apostol, Mathematical Analysis, Addison-Wesley, Reading MA., 1957.MATHGoogle Scholar
  2. 2.
    A. T. Bharucha-Reid, Random Integral Equations, Wiley, New York, 1970.Google Scholar
  3. 3.
    R. W. Brockett, Finite Dimensional Linear Systems, Wiley, New York, 1970.MATHGoogle Scholar
  4. 4.
    W. B. Davenport, Jr. and W. L. Root, An Introduction to the Theory of Random Signals and Noise, McGraw-Hill, New York, 1958.MATHGoogle Scholar
  5. 5.
    J. L. Doob, Stochastic Processes, Wiley, New York, 1953.MATHGoogle Scholar
  6. 6.
    J. Evans, “Preliminary Analysis of ELF Noise,” Tech. Note 1969–18, M.I.T. Lincoln Laboratory, Lexington, MA, March 1969.Google Scholar
  7. 7.
    P. M. Fishman, “Statistical Inference for Space-Time Point Processes,” D.Sc. Thesis, Sever Institute, Washington University, St. Louis, MO, June 1974.Google Scholar
  8. 8.
    R. H. Forrester and D. L. Snyder, “Phase-Tracking Performance of Direct-Detection Optical Receivers,” IEEE Trans, on Communications, Vol. COM-21, pp. 1037–1039, September 1973.CrossRefGoogle Scholar
  9. 9.
    R. Gagliardi and M. Haney, “Optical Synchronization - Phase Locking with Shot Noise Processes,” Tech. Rpt. USCEE - 396, Dep’t. of Electrical En- gineering, Univ. of Southern California, Los Angeles, CA, August 1970.Google Scholar
  10. 10.
    I. I. Gihman and A. Ja. Dorogovcev, “On Stability of Solutions of Stochastic Differential Equations,” Ukrain. Mat. Z, Vol. 17, pp. 229–250,1965.Google Scholar
  11. 11.
    I. I. Gihman and A. V. Skorokhod, Stochastic Differential Equations, Springer-Verlag, New York, 1972.MATHGoogle Scholar
  12. 12.
    I. Gikhman and A. Skorokhod, Introduction to the Theory of Random Processes, Saunders, Philadelphia, PA, 1969.Google Scholar
  13. 13.
    E. V. Hoversten, “Optical Communication Theory,” in: Laser Handbook (F. T. Arecchi and E. O. Schultz, Eds.), North Holland, Amsterdam, pp. 1805–1862,1972.Google Scholar
  14. 14.
    K. Itô, “On Stochastic Differential equations,” Mem. Am. Math. Soc. , No. 4, pp. 1–51,1951.Google Scholar
  15. 15.
    T. Kailath, Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, 1980.MATHGoogle Scholar
  16. 16.
    R. S. Kennedy, Fading Dispersive Communication Channels, Wiley, New York, 1969.Google Scholar
  17. 17.
    P. Langevin, “Sur La Theorie Du Mouvement Brownian,” C. R. Acad. Sci., Paris, Vol. 146, pp. 530–533,1908.MATHGoogle Scholar
  18. 18.
    W. C. Lindsey and M. K. Simon, Telecommunication Systems Engineering, Prentice-Hall, Englewood Cliffs, NJ, 1973.Google Scholar
  19. 19.
    R. S. Lipster and A. N. Shiryayev, Statistics of Random Processes I: General Theory, Springer-Verlag, New York, 1977.Google Scholar
  20. 20.
    R. S. Lipster and A. N. Shiryayev, Statistics of Random Processes I: Applications, Springer-Verlag, New York, 1978.Google Scholar
  21. 21.
    L. Liusternik and V. Sobolev, Elements of Functional Analysis, Ungar, New York, 1961.Google Scholar
  22. 22.
    A. Papoulis, “High Density Shot Noise and Gaussianity,” J. AppL Prob., Vol. 8, pp. 118–127, March 1971.MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    E. Parzen, Stochastic Processes, Holden-Day, San Francisco, CA, 1962.MATHGoogle Scholar
  24. 24.
    W. K. Pratt, Laser Communications Systems, Wiley, New York, 1969.Google Scholar
  25. 25.
    “Project West Ford,” Proc. IEEE, Vol. 52, May 1964.Google Scholar
  26. 26.
    A. V. Skorokhod, Studies in the Theory of Random Processes, Addison- Wesley, Reading, MA, 1964.Google Scholar
  27. 27.
    A. J. Viterbi, Principles of Coherent Communication, McGraw-Hill, New York, 1966.Google Scholar
  28. 28.
    E. Wong and B. Hajek, Stochastic Processes in Engineering Systems, Springer-Verlag, New York, 1985.MATHGoogle Scholar
  29. 29.
    L. A. Zadeh and C. A. Desoer, Linear System Theory, McGraw-Hill, New York, 1963.MATHGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1991

Authors and Affiliations

  • Donald L. Snyder
    • 1
  • Michael I. Miller
    • 1
  1. 1.Electronic Systems and Signals Research Laboratory, Department of Electrical EngineeringWashington UniversitySt. LouisUSA

Personalised recommendations