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. IACUS
Primo
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.
Inhomogeneous Poisson process; Minimax estimation; Primary 60K99; Random motions; Secondary 62M99; Telegraph equation
Settore SECS-S/01 - Statistica
2001
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/23726
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