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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.

MSC:

60K15 Markov renewal processes, semi-Markov processes
62P05 Applications of statistics to actuarial sciences and financial mathematics
93D20 Asymptotic stability in control theory
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