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Sampling and reconstruction of piecewise constant stochastic processes with Erlang stay time in states

  • Control in Stochastic Systems and Under Uncertainty Conditions
  • Published:
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Abstract

A statistical sampling and reconstruction procedure is developed for the class of stochastic processes indicated in the title. The Erlang phase method and recurrent recalculation for conditional Markov processes are used. Formulas for the a posteriori distribution of the transition time are obtained for the respective first moments and sampling interval. The procedures are easy-to-implement computationally. The influence of process parameters on the procedure parameters is analyzed. An illustrative example is given.

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References

  1. O. N. Novoselov and A. F. Fomin, Foundations of the Theory and Design of Information Systems (Mashinostroenie, Moscow, 1980) [in Russian].

    Google Scholar 

  2. A. I. Velichkin, Transmission of Analog Messages via Digital Channels (Radio i Svyaz’, Moscow, 1983) [in Russian].

    Google Scholar 

  3. V. I. Tikhonov and V. N. Kharisov, Statistical Analysis and Synthesis of Radio Devices and Systems (Radio i Svyaz’, Moscow, 1991) [in Russian].

    Google Scholar 

  4. Advanced Topics in Shannon Sampling and Interpolation Theory, Ed. by R. Marx (Springer, New York, 1992).

    Google Scholar 

  5. Nonuniform Sampling, Ed. by F. Marvasti (Kluwer, New York, 2001).

    MATH  Google Scholar 

  6. N. I. Kozlenko, Noise Immunity of Discrete Transmission of Continuous Data (Radiotekhnika, Moscow, 2004) [in Russian].

    Google Scholar 

  7. A. Jerry, “The Shannon Sampling Theorem—Its Various Extensions and Applications: A Tutorial Review,” in Proc. IEEE 65, 1565–1596(1977).

    Article  Google Scholar 

  8. A. Jerry, “Bibliography,” in Advanced Topics in Shannon Sampling and Interpolation Theory, Ed. by R. Marx (Springer, New York, 1992).

    Google Scholar 

  9. B. Lacaze, “Stationary Clock Changes on Stationary Process,” Signal Processing 55, 191 (1996).

    Article  MATH  Google Scholar 

  10. B. Lacaze, “Periodic Bi-Sampling of Stationary Processes,” Signal Processing 68, 283 (1998).

    Article  MATH  Google Scholar 

  11. B. Lacaze, “Non Uniform Sampling (Chapter 8)”, Ed. by F. Marvasti (Kluwer, New York, 2001).

    Google Scholar 

  12. V. A. Kazakov, USSR Inventor’s Certificate No. 756425, 1980.

  13. V. A. Kazakov, USSR Inventor’s Certificate No. 1023350, 1983.

  14. O. S. Amosov, “Markov Sequence Filtering on the Basis of Bayesian and Neural Network Approaches and Fuzzy Logic Systems in Navigation Data Processing,” J. Comput. Syst. Sci. Int. 43, 551–559 (2004).

    Google Scholar 

  15. A. V. Borisov, “Preliminary Distribution Analysis for the States of Special Control Systems with Random Structure,” J. Comput. Syst. Sci. Int. 44, 43–57 (2005).

    Google Scholar 

  16. A. V. Borisov and A. I. Stefanovich, “Optimal State Filtering of Controllable Systems with Random Structure,” J. Comput. Syst. Sci. Int. 46, 348–358 (2007).

    Article  MathSciNet  Google Scholar 

  17. V. A. Kazakov, “The Sampling-Reconstruction Procedure with a Limited Number of Samples of Stochastic Processes and Fields on the Basis of the Conditional Mean Rule,” Elektromagnitnye Volny Elektronnye Sistemy 10(1–2), 98 (2005).

    Google Scholar 

  18. V. A. Kazakov and Yu. A. Goritskii, “Discretization and Reconstruction of a Binary Markov Process,” Izv. Vyssh. Uchebn. Zaved., Radioelektronika, No. 11, 10–16 (2006).

  19. Yu. A. Goritskii and V. A. Kazakov, “Sampling-Reconstruction of Markov Processes with a Finite Number of States,” J. Comput. Syst. Sci. Int. 49, 16–21 (2010).

    Article  MathSciNet  Google Scholar 

  20. Yu. A. Goritskii and V. A. Kazakov, “A Discretization Procedure for Stochastic Processes with Linited Aftereffect,” Vestn. MEI, No. 6, 12–17 (2006).

  21. R. L. Stratonovich, Conditional Markov Processes and Their Application to the Theory of Optimal Control (Mosk. Gos. Univ., Moscow, 1966; Elsevier, New York, 1968).

    Google Scholar 

  22. E. M. Khazen, Methods of Optimal Statistical Decisions and Optimal Control Problems (Sovetskoe Radio, Moscow, 1968) [in Russian].

    Google Scholar 

  23. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Nauka, Moscow, 1971; Academic Press, New York, 1980).

    Google Scholar 

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Authors and Affiliations

  1. Moscow Power Engineering Institute, Krasnokazarmennaya ul. 14, Moscow, 111250, Russia

    Yu. A. Goritskii & V. A. Kazakov

  2. National Polytechnic Institute, Mexico City, Mexico

    Yu. A. Goritskii & V. A. Kazakov

Authors
  1. Yu. A. Goritskii
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  2. V. A. Kazakov
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Original Russian Text © Yu.A. Goritskii, V.A. Kazakov, 2011, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2011, No. 6, pp. 14–27.

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Goritskii, Y.A., Kazakov, V.A. Sampling and reconstruction of piecewise constant stochastic processes with Erlang stay time in states. J. Comput. Syst. Sci. Int. 50, 870–883 (2011). https://doi.org/10.1134/S1064230711060086

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  • DOI: https://doi.org/10.1134/S1064230711060086

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