Some new Chacon-Edgar-type inequalities for stochastic processes, and characterizations of Vitali-conditions

L. Egghe

Annales de l'I.H.P. Probabilités et statistiques (1980)

  • Volume: 16, Issue: 4, page 327-337
  • ISSN: 0246-0203

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Egghe, L.. "Some new Chacon-Edgar-type inequalities for stochastic processes, and characterizations of Vitali-conditions." Annales de l'I.H.P. Probabilités et statistiques 16.4 (1980): 327-337. <http://eudml.org/doc/77148>.

@article{Egghe1980,
author = {Egghe, L.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Vitali conditions; amart; stochastic lim sup; maximal inequality},
language = {eng},
number = {4},
pages = {327-337},
publisher = {Gauthier-Villars},
title = {Some new Chacon-Edgar-type inequalities for stochastic processes, and characterizations of Vitali-conditions},
url = {http://eudml.org/doc/77148},
volume = {16},
year = {1980},
}

TY - JOUR
AU - Egghe, L.
TI - Some new Chacon-Edgar-type inequalities for stochastic processes, and characterizations of Vitali-conditions
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1980
PB - Gauthier-Villars
VL - 16
IS - 4
SP - 327
EP - 337
LA - eng
KW - Vitali conditions; amart; stochastic lim sup; maximal inequality
UR - http://eudml.org/doc/77148
ER -

References

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  1. [1] K.A. Astbury, Amarts, indexed by directed sets. Ann. Prob., t. 6, 2, 1978, p. 267-278. Zbl0378.60017MR464394
  2. [2] A. Bellow, Uniform amarts: a class of asymptotic martingales for which strong almost sure convergence obtains. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, t. 41, 1978, p. 177-191. Zbl0391.60005MR471065
  3. [3] R. Cairoli, Une inégalité pour martingales à indices multiples et ses applications. Sém. de Prob., Univ. de Strasbourg. Lect. Notes in math., t. 124, 1970, p. 1-27, Springer-Verlag. Zbl0218.60045MR270424
  4. [4] R.V. Chacon, A « stopped » proof of convergence. Adv. in math., t. 14, 1974, p. 365-368. Zbl0308.60018MR365688
  5. [5] G.A. Edgar, Uniform semiamarts. Ann. de l'Institut H. Poincaré, t. 15, sect. B, 1979, p. 197-203. Zbl0423.60046MR563735
  6. [6] K. Krickeberg, Convergence of martingales with a directed index set. Trans. Am. Math. Soc., t. 83, 1956, p. 313-337. Zbl0083.27501MR91328
  7. [7] P. Mccartney, Neighborly bushes and the Radon-Nikodym-Property for Banach spaces, preprint 1979. Zbl0447.46012MR590873
  8. [8] P. Mccartney and R. O'Brien, A separable Banach space with the Radon-Nikodym-property which is not isomorphic to a subspace of a separable dual, preprint 1979. 
  9. [9] A. Millet et L. Sucheston, La convergence essentielle des martingales bornées dans L1 n'implique pas la condition de Vitali V. C. R. Acad. Sc. Paris, t. 288, série A, 1979, p. 595-598. Zbl0401.60044MR531590
  10. [10] A. Millet and L. Sucheston, Convergence of classes of amarts indexed by directed sets. Characterizations in terms of Vitali-conditions. Can. J. Math., t. 32, 1, 1980, p. 86-125. Zbl0448.60036MR559789
  11. [11] A. Millet and L. Sucheston, Characterizations of Vitali conditions with overlap in terms of convergence of classes of amarts. Can. J. Math., t. 31, 5, 1979, p. 1033-1046. Zbl0432.60059MR546956
  12. [12] A. Millet and L. Sucheston, A characterization of Vitali conditions in terms of maximal inequalities. Ann. Prob., t. 8, 2, 1980, p. 339-349. Zbl0428.60053MR566598
  13. [13] A. Millet and L. Sucheston, On convergence of L1-bounded martingales indexed by directed sets, preprint 1979. 
  14. [14] J. Neveu, Discrete parameter martingales. North Holland, Amsterdam; 1975. Zbl0345.60026MR402915

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