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 → ∞ in the first case; μ → ∞, with λ = βμ 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.

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

Martinucci, Barbara;
2020

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 → ∞ in the first case; μ → ∞, with λ = βμ 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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4748112
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