Rates of convergence in the functional CLT for multidimensional continuous time martingales

Stochastic Processes and their Applications

Volumn 91, Issue 1, 2001, Pages 57-76

  Courbot, B ^a  

^a UNIVERSITÉ DE RENNES 1   (France)

Author keywords

[No Author keywords available]

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EID: 0042403654     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(00)00054-5     Document Type: Article

References (28)

1. Berkes I., Philipp W. Approximation theorems for independent and weakly dependent random vectors. Ann. Probab. 7(1):1979;29-54.
2. Coquet F., Mémin J., Vostrikova L. Rate of convergence in the functional central limit theorem for likelihood ratio processes. Math. Methods Statist. 3(2):1994;89-113.
3. Courbot, B., 1998. Vitesses de convergence pour les martingales dans le théorème central limite fonctionnel: comparaison de méthodes, cadres uni et multidimensionnel. Thèse de doctorat de l'Université de Rennes I.
4. Courbot B. Rates of convergence in the functional CLT for martingales. C.R. Acad. Sci. Paris, Sér. I. 328:1999;509-513.
5. Courbot, B., 2000. Rates of convergence in the functional CLT for real martingales and applications to the multidimensional case. In: Proceedings of the Fourth Hungarian Colloquium on Limit Theorems of János Bolyai Mathematical Society, to appear.
6. Dudley R.M. Real Analysis and Probability. 1989;Wadsworth & Brooks Cole Mathematical Series, Pacific Grove, CA.
7. Eberlein E. Strong approximation of continuous time stochastic processes. J. Multivariate Anal. 31:1989;220-235.
8. Eberlein E., Römersperger M. Strong approximation of semimartingales and statistical processes. Probab. Theory Related Fields. 104:1996;539-567.
9. Fuk D.K., Nagaev S.V. Probability inequalities for sums of independent random variables. Theory Probab. Appl. 16(4):1971;643-660.
10. Haeusler E. An exact rate of convergence in the functional central limit theorem for special martingale difference arrays. Z. Wahrsch. Verw. Gebiete. 65:1984;523-534.
11. Haeusler, E., 1986. On the rate of convergence in ordinary and functional central limit theorems for martingales. In: Proceedings of the First World Congress of the Bernoulli Society, Vol. 1, Tashkent.
12. Hall P., Heyde C.C. Martingale Limit Theory and its Application. 1980;Academic Press, New York.
13. Jacod J., Mano P. Une évaluation de la distance entre les lois d'une semimartingale et d'un processus à accroissements indépendants. Stochastics. 25(2):1988;87-124.
14. Jacod J., Shiryaev A.N. Limit Theorems for Stochastic Processes. 1987;Springer, Berlin.
15. Komlós J., Major P., Tusnády G. An approximation of partial sums of independent RV's, and the sample DF. I. Z. Wahrsch. Verw. Gebiete. 32:1975;111-131.
16. Komlós J., Major P., Tusnády G. An approximation of partial sums of independent RV's, and the sample DF. II. Z. Wahrsch. Verw. Gebiete. 34:1976;33-58.
17. Kubilius K. Rate of convergence in the functional central limit theorem for semimartingales. Liet. Mat. Rinkinys. 25:1985;84-96.
18. Liptser R.S., Shiryaev A.N. Theory of Martingales. 1986;Kluwer Academic Publishers, Dordrecht.
19. Monrad D., Philipp W. Nearby variables with nearby conditionnal laws and a strong approximation theorem for Hilbert space valued martingales. Probab. Theory Related Fields. 88:1991;381-404.
20. Morrow G., Philipp W. An almost sure invariance principle for Hilbert space valued martingales. Trans. AMS. 273(1):1982;231-251.
21. Revuz D., Yor M. Continuous Martingales and Brownian Motion. 1994;Springer, Berlin.
22. Römersperger M. A note on nearby variables with nearby conditional laws. Probab. Theory Related Fields. 106:1996;371-377.
23. Sakhanenko, A.I., 1980. On unimprovable estimates of the rate of convergence in invariance principle. In: Nonparametric Statistical Inference, Colloquia Mathematica Societatis János Bolyai, Vol. 32, Budapest. North-Holland, Amsterdam, pp. 779-784.
24. Sakhanenko A.I. On estimates of the rate of convergence in the invariance principle. Borovkov A.A. Advances in Probability Theory: Limit Theorems and Related Problems. 1984;124-135 Springer, New York.
25. Sakhanenko A.I. Convergence rate in invariance principle for non-identically distributed variables with exponential moments. Borovkov A.A. Limit Theorems for Sums of Random Variables, Advances in Probability Theory. 1985;2-73 Springer, New York.
26. Zaitsev A.Y. Multidimensional version of the results of Komlós, Major and Tusnády for vectors with finite exponential moments. ESAIM, Probab. Statist. 2:1998;41-108.
27. Zaitsev, A.Y., 1998b. Multidimensional version of a result of Sakhanenko in the invariance principle for vectors with finite exponential moments. Preprint, Universität Bielefeld.
28. Zolotarev V.M. Probability metrics. Theory Probab. Appl. 28:1984;278-302.