Theory of Probability and Mathematical Statistics
Estimation of the remainder in asymptotic expansion of a functional of semi-Markov random evolution
V. S. Koroliuk, I. V. Samoilenko
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Abstract: In [5] we found regular and singular parts of the expansion for a functional of semi-Markov random evolution and showed regularity of initial conditions. In this work we estimate the remainder of the asymptotic expansion found in [5].
Keywords: asymptotic expansion, semi-Markov process, random evolution, remainder.
Bibliography: 1. S. Albeverio, V. S. Koroliuk, I. V. Samoilenko, Asymptotic expansion of semi-Markov random evolutions, Stochastics, 81 (2009), no. 5, 343-356.
2. V. S. Korolyuk, V. V. Korolyuk, Stochastic Models of Systems, Kluwer Acad. Publ., 1999.
3. V. S. Korolyuk, N. Limnios, Stochastic Systems in Merging Phase Space,World Scienti c Publishers, 2005.
4. V. S. Korolyuk, A. F. Turbin, Mathematical foundation of state lumping of large systems, Kluwer Acad. Publ., 1990.
5. V. S. Koroliuk, I. V. Samoilenko, Asymptotic expansion for a functional of semi-Markov random evolution in diffusion approximation scheme, Theory Probab. Math. Statist., 96 (2017), 84-99. (Ukrainian)
6. A. A. Pogorui, R. M. Rodriguez-Dagnino, Asymptotic expansion for transport processes in semi-Markov media, Theory Probab. Math. Statist., 83 (2011), 127-134.
7. I. V. Samoilenko, Asymptotic expansion for the functional of markovian evolution in Rd in the circuit of diffusion approximation, J. Appl. Math. Stoch. Anal., 3 (2005), 247-258.
8. I. V. Samoilenko, Asymptotic expansion of a semi-Markov random evolution, Ukr. Math. J., 58 (2006), no. 9, 1396-1414.
9. V. M. Shurenkov, Ergodic Markov processes, Nauka, Moscow, 1989. (Russian)
10. A. V. Swishchuk, Semi-Markov random evolutions: some ideas, methods and results, Exploring Stochastic Laws. Festschrift in Honour of the 70th Birthday of Academician V. S. Korolyuk (A. V. Skorokhod and Yu. V. Borovskikh, ed.), VSP, 1995, 417-442.
11. A. Swishchuk, Jianhong Wu, Evolution of Biological Systems in Random Media: Limit Theorems and Stability, Springer, 2003.
12. A. V. Swishchuk, Estimations of convergence rate in limi theorems for semi-Markov random evolutions, Stochastic systems and theor applications, Inst. of Math. NasUSSR, Kiev, 1990, 86-92. (Russian)
13. G. G. Yin, Q. Zhang, Continuous-Time Markov Chains and Applications: a Singular Perturbation Approach, Springer, 1998.
