Kingman's subadditive ergodic theorem

J. Michael Steele

Annales de l'I.H.P. Probabilités et statistiques (1989)

  • Volume: 25, Issue: 1, page 93-98
  • ISSN: 0246-0203

How to cite

top

Steele, J. Michael. "Kingman's subadditive ergodic theorem." Annales de l'I.H.P. Probabilités et statistiques 25.1 (1989): 93-98. <http://eudml.org/doc/77341>.

@article{Steele1989,
author = {Steele, J. Michael},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {subadditive ergodic theorem},
language = {eng},
number = {1},
pages = {93-98},
publisher = {Gauthier-Villars},
title = {Kingman's subadditive ergodic theorem},
url = {http://eudml.org/doc/77341},
volume = {25},
year = {1989},
}

TY - JOUR
AU - Steele, J. Michael
TI - Kingman's subadditive ergodic theorem
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1989
PB - Gauthier-Villars
VL - 25
IS - 1
SP - 93
EP - 98
LA - eng
KW - subadditive ergodic theorem
UR - http://eudml.org/doc/77341
ER -

References

top
  1. M.A. Ackoglu and L. Sucheston, A Ratio Ergodic Theorem for Superadditive Processes, Z. Wahr. Verw. Gebiete, Vol. 44, 1978, pp. 269-278. Zbl0386.60045MR509202
  2. M.A. Ackoglu and U. Krengle, Ergodic Theorems for Superadditive Processes, J. für die Reine und Angewante Math., Vol. 323, 1981, pp. 53-67. Zbl0453.60039MR611442
  3. D.L. Burkholder, Discussion of Prof. Kingman's paper, Ann. Probab., Vol. 1, 1973, pp. 900-902. MR356192
  4. A. DelJUNCO, On the Decomposition of a Subadditive Stochastic Process, Ann. Probability, Vol. 5, 1977, pp. 298-302. Zbl0362.60053MR443081
  5. J.G. Deken, Some Limit Result for Longest Common Subsequences, Discrete Math., Vol. 26, 1979, pp. 17-31. Zbl0403.68064MR535080
  6. Y. Derriennic, Sur le théorème ergodique sous-additif, C.R. Acad. Sci. Paris, T. 281, Series A, 1975, pp. 985-988. Zbl0327.60028MR396903
  7. Y. Derriennic, Quelques applications du théorème ergodique sous-additif, Astérisque, Vol. 74, 1980, pp. 183-201. Zbl0446.60059MR588163
  8. Y. Derriennic, Un théorème ergodique presque sous-additif, Ann. Probability, Vol. 11, 1983, pp. 669-677. Zbl0586.28014MR704553
  9. N. Ghoussoub and J.M. Steele, Vector Valued Subadditive Processes and Applications in Probability, Ann. Probability, Vol. 8, 1980, pp. 83-95. Zbl0426.60032MR556416
  10. T. Kamae, A Simple Proof of the Ergodic Theorem Using Non-Standard Analysis, Israel J. Math., Vol. 42, 1982, pp. 284-290. Zbl0499.28011MR682311
  11. Y. Katznelson and B. Weiss, A Simple Proof of Some Ergodic Theorems, Israel J. Math., Vol. 42, 1982, pp. 291-296. Zbl0546.28013MR682312
  12. J.F.C. Kingman, The Ergodic Theory of Subadditive Stochastic Processes, J. Roy. Statist. Soc. Ser., Vol. B30, 1968, pp. 499-510. Zbl0182.22802MR254907
  13. J.F.C. Kingman, Subadditive Ergodic Theory, Ann. Probability, Vol. 1, 1973, pp. 883-909. Zbl0311.60018MR356192
  14. J.F.C. Kingman, Subadditive Processes, Lecture Notes in Math., Vol. 539, 1976, pp. 167-223. Zbl0367.60030MR438477
  15. T. Ligget, An Improved Subadditive Ergodic Theorem, Ann. Probability, Vol. 13, 1985, pp. 1279-1285. Zbl0579.60023MR806224
  16. P. Loeb, Conversion from Non-Standard Measure Theory and Applications to Probability Theory, Transactions of the American Math. Soc., Vol. 211, 1975. MR390154
  17. E. Mourier, Éléments aléatoire dans un espace de Banach, Ann. Inst. H. Poincaré, 1953, pp. 161-244. Zbl0053.09503MR64339
  18. J. Moulin-Ollagnier, Théorème ergodique presque sous-additif et convergence en moyenne de l'information, Ann. Inst. Henri Poincaré, Vol. B 19, 1983, pp. 257-266. Zbl0524.28024MR725559
  19. J. Neveu, Courte demonstration du théorème ergodique sur-additif, Ann. Inst. Henri Poincaré, Vol. B 19, 1983, pp. 87-90. Zbl0507.60021MR699980
  20. D. Ornstein and B. Weiss, The Shannon-McMillan-Breiman Theorem for a Class of Amenable Groups, Israel J. Math., Vol. 44, 1983, pp. 53-60. Zbl0516.28020MR693654
  21. K. Schürger, A limit theorem for almost monotone sequences of random variables, Stochastic Processes and their Applications, Vol. 21, 1986, pp. 327-338. Zbl0608.60027MR833959
  22. K. Schürger, On Derrienic's almost subadditive ergodic theorem, Acta Math. Hungarica, Vol. 52, 1988 (to appear). Zbl0653.60028MR956142
  23. P. Shields, The Ergodic and Entropy Theorems Revisited, I.E.E.E. Transactions in Information Theory, IT-33 (2), 1987, pp. 263-265. Zbl0633.94004MR880168
  24. M.D. Smeltzer, Subadditive Stochastic Processes, Bull. Amer. Math. Soc., Vol. 83, 1977, pp. 1054-1055. Zbl0373.60043MR458585
  25. J.M. Steele, Empirical Processes and Subadditive Processes, Ann. Probability, Vol. 6, 1978, pp. 118-127. Zbl0374.60037MR464379

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.