Conditional Markov Renewal Theory I. Finite and Denumerable State Space
Lalley, S. P.
Ann. Probab., Tome 12 (1984) no. 4, p. 1113-1148 / Harvested from Project Euclid
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A renewal theory is developed for sums of independent random variables whose distributions are determined by the current state of a Markov chain (also known as "Markov additive" processes, or "semi-Markov" processes). This theory departs from existing theories in that its conclusions are required to be valid conditionally for a given realization of the Markov Chain. It rests on a peculiar coupling construction which differs markedly from existing coupling arguments.
Publié le : 1984-11-14
Classification:  Markov renewal theory,  coupling,  conditional limit theorem,  60K15,  60K05 
@article{1176993144,
     author = {Lalley, S. P.},
     title = {Conditional Markov Renewal Theory I. Finite and Denumerable State Space},
     journal = {Ann. Probab.},
     volume = {12},
     number = {4},
     year = {1984},
     pages = { 1113-1148},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993144}
}

Lalley, S. P. Conditional Markov Renewal Theory I. Finite and Denumerable State Space. Ann. Probab., Tome 12 (1984) no. 4, pp.  1113-1148. http://gdmltest.u-ga.fr/item/1176993144/