Swishchuk, A. V.; Goncharova, S. Ya. Stability of semi-Markov risk processes in the scheme of normal deviations. (English. Ukrainian original) Zbl 0958.60086 Theory Probab. Math. Stat. 59, 149-152 (1999); translation from Teor. Jmorvirn. Mat. Stat. 59, 144-147 (1998). Under some conditions a semi-Markov risk process in series scheme converges to the averaged and the diffusion risk processes which are the first and the second approximation, respectively, to the initial semi-Markov risk process. Asymptotic stability in mean square is established for the normal lattice deviated risk process. Analogous stability is investigated for semi-Markov risk process in series scheme. Reviewer: M.P.Moklyachuk (Kyïv) MSC: 60K15 Markov renewal processes, semi-Markov processes 62P05 Applications of statistics to actuarial sciences and financial mathematics 93D20 Asymptotic stability in control theory Keywords:semi-Markov process; stochastic stability; normal deviations scheme PDFBibTeX XMLCite \textit{A. V. Swishchuk} and \textit{S. Ya. Goncharova}, Teor. Ĭmovirn. Mat. Stat. 59, 144--147 (1998; Zbl 0958.60086); translation from Teor. Jmorvirn. Mat. Stat. 59, 144--147 (1998)