Abstract
We consider a telegraph process with elastic boundary at the origin studied recently in the literature (see e.g. Di Crescenzo et al. (Methodol Comput Appl Probab 20:333–352 2018)). It is a particular random motion with finite velocity which starts at x ≥ 0, and its dynamics is determined by upward and downward switching rates λ and μ, with λ > μ, and an absorption probability (at the origin) α ∈ (0,1]. Our aim is to study the asymptotic behavior of the absorption time at the origin with respect to two different scalings: \(x\to \infty \) in the first case; \(\mu \to \infty \), with λ =β μ for some β > 1 and x > 0, in the second case. We prove several large and moderate deviation results. We also present numerical estimates of β based on an asymptotic Normality result for the case of the second scaling.
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The authors acknowledge the support of: GNAMPA and GNCS groups of INdAM (Istituto Nazionale di Alta Matematica); MIUR–PRIN 2017, Project ‘Stochastic Models for Complex Systems’ (no. 2017JFFHSH); MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata (CUP E83C18000100006).
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Macci, C., Martinucci, B. & Pirozzi, E. Asymptotic Results for the Absorption Time of Telegraph Processes with Elastic Boundary at the Origin. Methodol Comput Appl Probab 23, 1077–1096 (2021). https://doi.org/10.1007/s11009-020-09804-y
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DOI: https://doi.org/10.1007/s11009-020-09804-y