# Statistical analysis of the inhomogeneous telegrapher's process

*Stefano Iacus* ()

*Statistics & Probability Letters*, 2001, vol. 55, issue 1, 83-88

**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. 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.

**Keywords:** Telegraph; equation; Inhomogeneous; Poisson; process; Minimax; estimation; Random; motions (search for similar items in EconPapers)

**Date:** 2001

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