Estimation of the distribution for the change-point of a continuous homogeneous Markov process. (Russian) Zbl 0666.60075

Mazhuga, Yu. I.

Teor. Veroyatn. Mat. Stat., Kiev 39, 83-87 (1988).

Some estimates of the distributions of life times for homogeneous Markov processes with general state spaces are given.
For example, denote by \(\zeta\) the life time and \(m(x)=E^ x\zeta\). Suppose that \(\pi\) is an excessive probability measure, \(E^{\pi}\zeta <\infty\), and the initial distribution \(\alpha\leq a\pi\), where a is a constant. Then for each \(m>0\) \[ \sup_{t\geq 0}| P_{\alpha}(\zeta >t)-e^{-t/m}\leq (2a/m)\int \pi (dx)| m(x)-m. \]

Reviewer: He Shengwu

MSC:

60J75	Jump processes (MSC2010)
62M09	Non-Markovian processes: estimation

Keywords:

distributions of life times; Markov processes; excessive probability measure