Perturbation approach to scaled type Markov renewal processes with infinite mean

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Pajor-Gyulai, Zsolt; Szász, Domokos;
  • Subject: Mathematics - Probability | 60K15 and 60F99 | Mathematics - Dynamical Systems

Scaled type Markov renewal processes generalize classical renewal processes: renewal times come from a one parameter family of probability laws and the sequence of the parameters is the trajectory of an ergodic Markov chain. Our primary interest here is the asymptotic d... View more
  • References (20)
    20 references, page 1 of 2

    [1] K.K. Anderson, K.B. Athreya A renewal theorem in the infinite mean case. Ann. Prob. 15, 388-393 (1987)

    [2] V.S. Barbu, N. Limnios Semi-Markov Chains and Hidden Semi-Markov Models toward Applications, Their Use in Reliability and DNA Analysis, Springer (ISBN 978-0-387-73171-1), (2008)

    [3] E. Cinlar. Markov renewal theory. Adv. in Appl. Probab., 1:123-187, (1969)

    [4] E. Cinlar. Introduction to Stochastic Processes. Prentice Hall, New York, (1975)

    [5] R. Durrett. Probability. Theory&Examples, Duxburry Press, 3rd Edition, (2005)

    [6] E.B. Dynkin Some limit theorems for sums of independent random variables with infinite mathematical expectations. Izv.Akad.Nauk. SSSR Ser.Mat. 19, 247-266 (1955) (in Russian). English translation: Selected Translations, Math. Statist. Prob.1,171-189 (1961)

    [7] K.B.Erickson Strong renewal theorems with infinite mean Trans. Amer. Math. Soc. 151, 263-291 (1970)

    [8] W. Feller. An Introduction to Probability Theory and Its Applications, Volume II, 2nd Ed. John Wiley&Sons, Inc. (1971)

    [9] Janssen J. (ed) Semi-Markov Models. Theory and Applications Plenum Press New York. (1986)

    [10] Janssen J., Limnios N. Semi-Markov Models and Applications. Kluwer Academic New York. (1999)

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