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.

我们考虑了文献中最近研究的，起源处具有弹性边界的电报过程（例如，参见Di Crescenzo等人（Methodol Comput Appl Probab 20：333–352 2018））。它是具有有限速度，其开始于所述特定的随机运动X ≥0，并且它的动力学是由向上和向下的开关速率确定λ和μ，与λ > μ和吸收概率（在原点）α＆Element;（0， 1]。我们的目的是针对两种不同的标度研究原点处吸收时间的渐近行为：第一种情况为\（x \ to \ infty \） ; \（\ mu \ to \ infty \），用λ =β μ在第二种情况下，对于某些β> 1和x > 0的情况。我们证明了几个大的和中等的偏差结果。对于第二缩放的情况，我们还基于渐近正态性结果给出了β的数值估计。