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Probability density of a stochastic process at the output of a linear system

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Abstract

We propose and analyze a method of direct statistical analysis for linear first-order systems with deterministic parameters. We derive the one- and multi-dimensional (with arbitrary dimension n) probability density of a stochastic process at the output of a linear system.

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References

  1. B. R. Levin,Theoretical Foundation of Statistical Radio Engineering [in Russian], Sovet-skoe Radio, Moscow (1969).

    Google Scholar 

  2. V. I. Tikhonov,Statistical Radio Engineering [in Russian], Radio i Svyaz’, Moscow (1982), p. 680.

    Google Scholar 

  3. P. I. Kuznetsov, R. L. Stratonovich, and V. I. Tikhonov,Dokl. Akad. Nauk 94, No. 4, 615 (1954).

    MATH  Google Scholar 

  4. A. N. Malakhov,Cumulant Analysis of Stochastic Non-Gaussian Processes and their Transformations [in Russian], Sovet-skoe Radio, Moscow (1978).

    MATH  Google Scholar 

  5. Sh. M. Chebdarov and A. T. Trofimov,Radiotech. Elektron.,20, No. 4, 734 (1975).

    Google Scholar 

  6. M. A. Meyer and D. Middleton,J. Appl. Phys.,25 No. 8, 1037 (1954).

    Article  MATH  ADS  Google Scholar 

  7. V. A. Solodov,Linear Systems of Automatic Control with Variable Parameters [in Russian], Fizmatgiz, Moscow (1962).

    Google Scholar 

  8. I. N. Amiantov,Selected Problems of Statistical Theory of Communication [in Russian]. Sovet-skoe Radio, Moscow (1971).

    Google Scholar 

  9. V. I. Esipenko and O. B. Shchuko, “One-Dimensional Probability Density of the Sum of Random Quantities,” Preprint No. 345, Nizhny Novgorod, Radiophysical Research Institute (1992).

  10. I. M. Gel’fand and G. E. Shilov,Generalized Functions and Actions with the Latter [in Russian], Fizmatgiz, Moscow (1959).

    Google Scholar 

  11. G. Cramer,Mathematical Methods of Statistics [Russian translation], Inostrannaya Literatura, Moscow (1948).

    Google Scholar 

  12. Ya. Mikusinskii and R. Sikorskii,Elementary Theory of Generalized Functions [Russian translation], Inostrannaya Literatura, Moscow (1959).

    Google Scholar 

  13. A. N. Malakhov,Fluctuations in Self-Oscillating Systems [in Russian], Nauka, Moscow (1968).

    Google Scholar 

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Authors
  1. V. I. Esipenko
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Additional information

Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 3, pp. 287–300, March 1999.

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Esipenko, V.I. Probability density of a stochastic process at the output of a linear system. Radiophys Quantum Electron 42, 257–268 (1999). https://doi.org/10.1007/BF02678849

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  • DOI: https://doi.org/10.1007/BF02678849

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