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 =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.
Asymptotic Results for the Absorption Time of Telegraph Processes with Elastic Boundary at the Origin
Pirozzi E.
2021
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 =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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
