On an asymptotic representation of a normalizing factor for a random matrix-valued evolution. (English. Ukrainian original) Zbl 0998.60086

Nishchenko, I. I.

Theory Probab. Math. Stat. 64, 153-160 (2002); translation from Teor. Jmovirn. Mat. Stat. 64, 129-135 (2001).

Let \(\{N^{\varepsilon}(t),\varepsilon>0\}\) be a family of random matrix-valued evolutions constructed by a family of stochastically continuous nonnegative random processes depending on a small parameter. The author studies the asymptotic behaviour of the normalizing multiplier \(\rho^{\varepsilon}\) such that there is a finite limit as \(\varepsilon \to 0\) of the mathematical expectation \(EN^{\varepsilon}(\cdot)\) under the time scale parameter change \(t/\rho^{\varepsilon}\).

Reviewer: N.M.Zinchenko (Kyïv)

MSC:

60K15

Markov renewal processes, semi-Markov processes

Keywords:

random evolution; random process; small parameter; mathematical expectation