Uniform and ratio limit theorems for Markov renewal and semi-regenerative processes on a general state space

E. Nummelin

Annales de l'I.H.P. Probabilités et statistiques (1978)

  • Volume: 14, Issue: 2, page 119-143
  • ISSN: 0246-0203

How to cite

top

Nummelin, E.. "Uniform and ratio limit theorems for Markov renewal and semi-regenerative processes on a general state space." Annales de l'I.H.P. Probabilités et statistiques 14.2 (1978): 119-143. <http://eudml.org/doc/77083>.

@article{Nummelin1978,
author = {Nummelin, E.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Renewal Process; Recurrence Time; Renewal Theorems; Ratio Limit Theorems; Splitting Technique},
language = {eng},
number = {2},
pages = {119-143},
publisher = {Gauthier-Villars},
title = {Uniform and ratio limit theorems for Markov renewal and semi-regenerative processes on a general state space},
url = {http://eudml.org/doc/77083},
volume = {14},
year = {1978},
}

TY - JOUR
AU - Nummelin, E.
TI - Uniform and ratio limit theorems for Markov renewal and semi-regenerative processes on a general state space
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1978
PB - Gauthier-Villars
VL - 14
IS - 2
SP - 119
EP - 143
LA - eng
KW - Renewal Process; Recurrence Time; Renewal Theorems; Ratio Limit Theorems; Splitting Technique
UR - http://eudml.org/doc/77083
ER -

References

top
  1. [1] E. Arjas, E. Nummelin and R.L. Tweedie, Uniform limit theorems for non-singular renewal and Markov renewal processes. 1976. To appear in J. Appl. Prob. Zbl0375.60095MR467955
  2. [2] M.R. Blumenthal and R.K. Getoor, Markov Processes and Potential Theory. Academic Press, New York, 1968. Zbl0169.49204MR264757
  3. [3] E. Cinlar, Periodicity in Markov renewal theory. Adv. Appl. Prob., t. 6, p. 61-78. Zbl0281.60104MR359056
  4. [4] R. Cogburn, A uniform theory for sums of Markov chain transition probabilities. Ann. Probability, t. 3, 1975, p. 191-214. Zbl0348.60106MR378103
  5. [5] J.L. Doob, Stochastic processes. Wiley and Sons, New York, 1953. Zbl0053.26802MR58896
  6. [6] M. Duflo and D. Revuz, Propriétés asymptotiques des probabilités de transition des processus de Markov récurrents. Ann. Inst. Henri Poincaré, Sect. B, t. V, 1969, p. 233-244. Zbl0183.47003MR273680
  7. [7] J. Jacod, Théorème de renouvellement et classification pour les chaînes semi-markoviennes. Ann. Inst. Henri Poincaré, Sect. B, t. VII, 1971, p. 83-129. Zbl0217.50502MR305496
  8. [8] J. Jacod, Corrections et compléments à l'article : « Théorème de renouvellement et classification pour les chaînes semi-markoviennes ». Ann. Inst. Henri Poincaré, Sect. B, t. X, 1974, p. 201-209. Zbl0306.60058MR353486
  9. [9] H. Kesten, Renewal theory for functionals of a Markov chain with general state space. Ann. Probability, t. 2, 1974, p. 355-386. Zbl0303.60090MR365740
  10. [10] D. Mcdonald, On semi-Markov and semi-regenerative processes I. 1976, to appear. Zbl0395.60080MR491492
  11. [11] D. Mcdonald, On semi-Markov and semi-regenerative processes II. 1976, to appear. Zbl0395.60081MR491492
  12. [12] M. Métivier, Théorème limite quotient pour les chaînes de Markov récurrentes au sens de Harris. Ann. Inst. Henri Poincaré, Sect. B, t. VIII, 1972, p. 93-105. Zbl0271.60069MR305483
  13. [13] J. Neveu, Potentiel markovien récurrent des chaînes de Harris. Ann. Inst. Fourier, t. 22, 1972, p. 85-130. Zbl0226.60084MR380992
  14. [14] J. Neveu, Généralisation d'un théorème limite-quotient, in : Trans. 6th Prague Conf. on Inf. Theory, Stat. Dec. Funct., Random Proc. (Czech. Acad. Sci., Prague), 1973. Zbl0284.60063MR350859
  15. [15] E. Nummelin, A splitting technique for φ-recurrent Markov chains. 1976, to appear. 
  16. [16] E. Nummelin, On the Poisson equation for φ-recurrent Markov chains. Preprint, Helsinki University of Technology, 1976. 
  17. [17] S. Grey, Limit theorems for Markov chain transition probabilities. Van Nostrand, New York, 1971. 
  18. [18] R. Pyke and R. Schaufele, Limit theorems for Markov renewal processes. Ann. Math. Statist., t. 35, 1964, p. 1746-1764. Zbl0134.34602MR168026
  19. [19] D. Revuz, Markov chains. North-Holland, Amsterdam, 1975. Zbl0332.60045MR415773

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.