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Statistical analysis of the inhomogeneous telegrapher's process

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  • Stefano Iacus

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Abstract

We consider a problem of estimation for the telegrapher's process on the line, say X(t), driven by a Poisson process with non constant rate. It turns out that the finite-dimensional law of the process X(t)is a solution to the telegraph equation with non constant coefficients. We give the explicit law (P) of the process X(t) for a parametric class of intensity functions for the Poisson process. We propose anestimator for the parameter of P and we discuss its properties as a first attempt to apply statistics to these models.

Suggested Citation

  • Stefano Iacus, 2001. "Statistical analysis of the inhomogeneous telegrapher's process," Departmental Working Papers 2001-02, Department of Economics, Management and Quantitative Methods at Universit√† degli Studi di Milano.
  • Handle: RePEc:mil:wpdepa:2001-02
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    File URL: http://wp.demm.unimi.it/files/wp/2001/DEMM-2001_002wp.pdf
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    References listed on IDEAS

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    1. Foong, S. K. & Kanno, S., 1994. "Properties of the telegrapher's random process with or without a trap," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 147-173, September.
    2. Orsingher, Enzo, 1985. "Hyperbolic equations arising in random models," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 93-106, December.
    3. Orsingher, Enzo, 1990. "Probability law, flow function, maximum distribution of wave-governed random motions and their connections with Kirchoff's laws," Stochastic Processes and their Applications, Elsevier, vol. 34(1), pages 49-66, February.
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    Cited by:

    1. De Gregorio, Alessandro & Macci, Claudio, 2012. "Large deviation principles for telegraph processes," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1874-1882.
    2. Alessandro Gregorio & Stefano Iacus, 2008. "Parametric estimation for the standard and geometric telegraph process observed at discrete times," Statistical Inference for Stochastic Processes, Springer, vol. 11(3), pages 249-263, October.
    3. De Gregorio, Alessandro, 2009. "Parametric estimation for planar random flights," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2193-2199, October.
    4. Johan GB Beumee & Chris Cormack & Peyman Khorsand & Manish Patel, 2014. "Path Diffusion, Part I," Papers 1406.0077, arXiv.org.
    5. Macci, Claudio, 2016. "Large deviations for some non-standard telegraph processes," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 119-127.
    6. Nicole Bauerle & Igor Gilitschenski & Uwe D. Hanebeck, 2014. "Exact and Approximate Hidden Markov Chain Filters Based on Discrete Observations," Papers 1411.0849, arXiv.org, revised Dec 2014.

    More about this item

    Keywords

    telegraph equation; inhomogeneous Poisson process; minimax;

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