2007/05/03 by Alessandro De Gregorio, Stefano M. Iacus, De Gregorio, Alessandro +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Mathematical Biology Tumor Growth #Methodology (stat.ME) #Probability (math.PR) #Statistical Finance (q-fin.ST) #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.0705.0503
openalex publication_date 2007/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant velocity + v or -v. The changes of direction are governed by an homogeneous Poisson process with rate λ>0. In this paper, we consider a change point estimation problem for the rate of the underlying Poisson process by means of least squares method. The consistency and the rate of convergence for the change point estimator are obtained and its asymptotic distribution is derived. Applications to real data are also presented.