Asymptotic Results for the Absorption Time of Telegraph Processes with Elastic Boundary at the Origin

Claudio Macci (), Barbara Martinucci () and Enrica Pirozzi ()
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Claudio Macci: Università di Roma Tor Vergata
Barbara Martinucci: Università degli Studi di Salerno
Enrica Pirozzi: Università di Napoli Federico II

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 3, 1077-1096

Abstract: 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 → ∞ $x\to \infty $ in the first case; μ → ∞ $\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.

Keywords: Finite velocity; Random motion; Large deviations; Moderate deviations; 60F10; 60J25; 60K15 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-020-09804-y

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