Statistical analysis of the inhomogeneous telegrapher's process
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. The finite-dimensional law of the process X(t) is a solution to the telegraph equation with non-constant coefficients. We present the explicit law (P[theta]) of the process X(t) for a parametric class of intensity functions for the Poisson process. This is one rare example where an explicit law can be obtained. We propose further, an estimator for the parameter [theta] of P[theta] and we discuss its properties as a first attempt to apply statistics to these models.
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Volume (Year): 55 (2001)
Issue (Month): 1 (November)
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References listed on IDEAS
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- 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.
- Orsingher, Enzo, 1985. "Hyperbolic equations arising in random models," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 93-106, December.
- 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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