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Lower estimation error bounds for Gauss-Poisson processes

  • Adrian Segall
Part II: Research Reports
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 16)

Abstract

The paper considers the problem of estimation of a signal modulating the rate of an observed jump process. Representation formulas for the least squares estimate have been obtained in previous works, but the exact solution requires solving an infinite set of stochastic differential equations, so that one has to work with suboptimal estimates. In order to investigate their performance compared with the optimal estimate, bounds for the performance of the latter are useful. In this paper we apply a general method developed by Bobrovsky-Zakai to obtain lower bounds for the estimation error when the observed process is of the Gauss-Poisson type.

Keywords

Stochastic Differential Equation Jump Process Independent Increment Stochastic Control Problem Lower Estimation Bound 
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.

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References

  1. 1.
    A. Segall, The modelling of adaptive routing in data-communication networks, IEEE Trans. on Comm, Vol. COM-25, No.1, Jan. 1977.Google Scholar
  2. 2.
    A. Segall, Centralized and decentralized control schemes for Gauss-Poisson processes, IEEE Trans. on Autom. Control. Vol. AC-23, No.1, Feb. 1978.Google Scholar
  3. 3.
    D.L. Snyder & P.M. Fishman, How to track a swarm of fireflies by observing their flashes, IEEE Trans. on Infor. Theory, Vol. IT-21, Nov. 1975.Google Scholar
  4. 4.
    D.L. Snyder, I.B. Rhodes and E.V. Hovesten, A separation theorem for stochastic control problems with point process observations, Automatica, Vol. 13, Jan. 1977.Google Scholar
  5. 5.
    M. Vaca and D.L. Snyder, A measure transformation approach to estimation and decision for observations derived from martingales, Wash. Univ. School of Medicine, Mono. 271, May 1975.Google Scholar
  6. 6.
    I.B. Rhodes and D.L. Snyder, Estimation and control performance for space — time point process observations, IEEE Trans. Autom. Control. Vol. AC-22, No. 3, June 1977.Google Scholar
  7. 7.
    B.Z. Bobrovsky & M. Zakai, A lower bound on the estimation error for certain diffusion processes, IEEE Trans. Infor. Thry. Vol. IT-22, No. 1, Jan. 1976.Google Scholar
  8. 8.
    A.V. Skorokhod, Random processes with independent increments, DDC Report AD645769, Aug. 1966.Google Scholar
  9. 9.
    A.V. Skorokhod, On the differentiability of measures corresponding to random processes, II Markov processes, Theory Prob. Appl. (USSR), Vol. V, No.1, 1960(sec.4).Google Scholar
  10. 10.
    A. Segall & T. Kailath, Radon-Nikodym derivatives with respect to measures induced by discontinuous independent increment processes, Ann. of Prob., Vol. 3, No.3, June 1975.Google Scholar
  11. 11.
    A. Segall & T. Kailath, The modelling of randomly modulated jump processes, IEEE Trans. on Infor. Thry, Vol. IT-21, No.2, March 1975.Google Scholar
  12. 12.
    K.L. Chung, A course in probability theory, Harcourt, Brace & World, 1968.Google Scholar
  13. 13.
    A. Segall, Stochastic processes in estimation theory, IEEE Trans. Infor. Thry. Vol. IT-22, No. 3, May 1976.Google Scholar
  14. 14.
    A. Segall & T. Kailath, Martingales in nonlinear least-squares estimation theory, in E. Stear, Advances in Nonlinear Estimation, to appear.Google Scholar
  15. 15.
    A. Segall, On estimation error bounds for jump prcesses, in preparation.Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Adrian Segall
    • 1
  1. 1.Department of Electrical Engineering TechnionIsrael Institute of TechnologyHaifaIsrael

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