Kolmogorov matrix, and a continuous Markov chain with a finite number of states
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 503-509
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In terms of ergodicity of averaged systems with constant coefficients (and Kolmogorov matrix), the signs of ergodicity of continuous Markov chains with a finite number of States with periodic and almost periodic coefficients are indicated.
Keywords: Kolmogorov matrices, continuous Markov chains with periodic and almost periodic coefficients.
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A. I. Perov. Kolmogorov matrix, and a continuous Markov chain with a finite number of states. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 503-509. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a19/

[1] E. Hille, R. Phillips, Functional Analysis and Semigroups, Moscow, 1962, 832 pp. (In Russian)

[2] E. L. Blokh, L. I. Loshinskiy, V. Ya. Turin, The Basics of Linear Algebra and Some of Its Applications, Vysshaya Shkola Publ., Moscow, 1971, 216 pp. (In Russian)

[3] A. I. Perov, “Signs of ergodicity of Kolmogorov almost periodic systems”, Proceedings of the Russian Academy of Sciences, 380:1 (2001), 9–12 (In Russian) | MR

[4] A. I. Perov, “Signs of ergodicity of Markov almost periodic systems”, Proceedings of the Russian Academy of Sciences, 384:4 (2002), 455–459 (In Russian) | MR

[5] R. Bellman, Introduction to the Theory of Matrices, Nauka Publ., Moscow, 1969, 369 pp. (In Russian) | MR

[6] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1967, 576 pp. | MR

[7] B. P. Demidovich, Lectures on Mathematical Stability Theory, Nauka Publ., Moscow, 1967, 472 pp. (In Russian) | MR

[8] F. R. Gantmacher, M. G. Krein, Oscillatory Matrices and Kernels and Small Oscillations of Mechanical Systems, State Publ. of Technical and Theoretical Literature, Moscow–Leningrad, 1950, 360 pp. (In Russian) | MR

[9] E. Seneta, Non-negative Matrices and Markov Chains, Springer, Sydney, 2006, 292 pp. | MR