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Markov renewal theorems in a scheme of series


Four Markov renewal type theorems in the scheme of series are proved.

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Literature cited

  1. 1.

    V. M. Shurenkov, Ergodic Markov Processes [in Russian], Nauka, Moscow (1989).

  2. 2.

    T. Kato, Theory of Perturbations of Linear Operators [Russian translation], Mir, Moscow (1972).

  3. 3.

    S. G. Krein (ed.), Functional Analysis [in Russian], Nauka, Moscow (1972).

  4. 4.

    N. V. Kartashov, “Inequalities in orgodicity and stability theorems for Markov chains with general phase space. I,” Teor. Veroyatn. Primen.,30, No. 2, 230–240 (1985).

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1443–1448, November, 1990.

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Alimov, D., Shurenkov, V.M. Markov renewal theorems in a scheme of series. Ukr Math J 42, 1283–1288 (1990).

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  • Type Theorem
  • Renewal Theorem
  • Renewal Type
  • Markov Renewal Theorem