Estimates for parameters of deformation of observations over Markov systems. (Ukrainian, English) Zbl 1051.62068

Voĭna, O. A.; Zhigaĭlo, O. O.

Teor. Jmovirn. Mat. Stat. 67, 1-8 (2002); translation in Theory Probab. Math. Stat. 67, 1-10 (2003).

Suppose that functioning of a system can be described by a Markov process with continuous time and finite phase space, observations over the transient moments are deformed by the functions \(D(t)=D(t,\theta)=\{d_i(t,\theta)\), \(t\geq 0\), \(i\in E \}\) depending on the unknown vector parameter \(\theta=(\theta_1,\dots,\theta_r)\) and the state \(i\) of the system, but there is no information about the state \(i\) of the system. The authors propose consistent estimates for \(\theta=(\theta_1,\dots,\theta_r)\) and obtain conditions for their asymptotic normality.

Reviewer: N. M. Zinchenko (Kyïv)

MSC:

62M05	Markov processes: estimation; hidden Markov models
62N05	Reliability and life testing
62N02	Estimation in survival analysis and censored data

Keywords:

Markov system; limit theorem; deformation of observations; transient moment; consistent estimate