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 (Pθ) 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 θ of Pθ and we discuss its properties as a first attempt to apply statistics to these models.
Statistic analysis of the inhomogeneous telegrapher's process / S.M. IACUS. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - 55:1(2001), pp. 83-88.
Statistic analysis of the inhomogeneous telegrapher's process
S.M. IACUSPrimo
2001
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 (Pθ) 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 θ of Pθ and we discuss its properties as a first attempt to apply statistics to these models.Pubblicazioni consigliate
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