论文标题
电报过程具有弹性边界的吸收时间的渐近结果
Asymptotic results for the absorption time of telegraph processes with elastic boundary at the origin
论文作者
论文摘要
我们考虑了最近在文献中研究的弹性边界的电报过程。这是一个特定的随机运动，具有有限速度，从$ x \ geq 0 $开始，其动态由向上和向下的切换速率$λ$和$μ$，$λ>μ$ $ $ $ $ $，以及吸收概率（在原点上）$α\ in（0,1] $。我们的目的是在（0,1] $。 $ x \ to \ infty $在第一个情况下； $μ=β$，对于某些$β> 1 $和$ x> 0 $，在第二个情况下，我们也证明了几个大型和中等的偏差结果。
We consider a telegraph process with elastic boundary at the origin studied recently in the literature. It is a particular random motion with finite velocity which starts at $x\geq 0$, and its dynamics is determined by upward and downward switching rates $λ$ and $μ$, with $λ>μ$, and an absorption probability (at the origin) $α\in(0,1]$. 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; $μ\to\infty$, 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.
