Large deviations of U-empirical measures in strong topologies and applications
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 5, pp. 779-797.
@article{AIHPB_2002__38_5_779_0,
     author = {Eichelsbacher, Peter and Schmock, Uwe},
     title = {Large deviations of $U$-empirical measures in strong topologies and applications},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {779--797},
     publisher = {Elsevier},
     volume = {38},
     number = {5},
     year = {2002},
     zbl = {1033.60033},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_2002__38_5_779_0/}
}
TY  - JOUR
AU  - Eichelsbacher, Peter
AU  - Schmock, Uwe
TI  - Large deviations of $U$-empirical measures in strong topologies and applications
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2002
SP  - 779
EP  - 797
VL  - 38
IS  - 5
PB  - Elsevier
UR  - http://archive.numdam.org/item/AIHPB_2002__38_5_779_0/
LA  - en
ID  - AIHPB_2002__38_5_779_0
ER  - 
%0 Journal Article
%A Eichelsbacher, Peter
%A Schmock, Uwe
%T Large deviations of $U$-empirical measures in strong topologies and applications
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2002
%P 779-797
%V 38
%N 5
%I Elsevier
%U http://archive.numdam.org/item/AIHPB_2002__38_5_779_0/
%G en
%F AIHPB_2002__38_5_779_0
Eichelsbacher, Peter; Schmock, Uwe. Large deviations of $U$-empirical measures in strong topologies and applications. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 5, pp. 779-797. http://archive.numdam.org/item/AIHPB_2002__38_5_779_0/

[1] A. De Acosta, On large deviations of empirical measures in the τ-topology, J. Appl. Probab. 31A (1994) 41-47, (special volume). | Zbl

[2] R. Azencott, Grandes Déviations et Applications, Lectures Notes in Mathematics, 774, Springer-Verlag, Berlin, 1980. | MR | Zbl

[3] R.R. Bahadur, S.L. Zabell, Large deviations of the sample mean in general vector spaces, Ann. Probab. 7 (1979) 587-621. | MR | Zbl

[4] Z. Baranyai, On the factorisation of the complete uniform hypergraph, in: Hajnal A., Rado T., Sós V.T. (Eds.), Infinite and Finite Sets, North-Holland, Amsterdam, 1975, pp. 91-108. | MR | Zbl

[5] Yu.V. Borovskikh, U-Statistics in Banach Spaces, VSP, Utrecht, 1996. | MR | Zbl

[6] S.D. Chatterji, Martingale convergence and the Radon-Nikodým theorem in Banach spaces, Math. Scand. 22 (1) (1968) 21-41. | Zbl

[7] I. Csiszár, I-divergence geometry of probability distributions and minimization problems, Ann. Probab. 3 (1) (1975) 146-158. | MR | Zbl

[8] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, Springer-Verlag, New York, 1998. | MR | Zbl

[9] J.-D. Deuschel, D.W. Stroock, Large Deviations, Pure and Applied Mathematics, 137, Academic Press, San Diego, 1989. | MR | Zbl

[10] M.D. Donsker, S.R.S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time III, Comm. Pure Appl. Math. 29 (1976) 389-461. | MR | Zbl

[11] H. Dym, H.P. Mckean, Fourier Series and Integrals, Academic Press, New York and London, 1972. | MR | Zbl

[12] P. Eichelsbacher, Large deviations for products of empirical probability measures in the τ-topology, J. Theoret. Probab. 10 (3) (1997) 903-929. | Zbl

[13] P. Eichelsbacher, M. Löwe, Large deviation principle for m-variate von Mises-statistics and U-statistics, J. Theoret. Probab. 8 (1995) 807-824. | MR | Zbl

[14] P. Eichelsbacher, U. Schmock, Rank-dependent moderate deviations of U-empirical measures in strong topologies, submitted to Probab. Theor. Relat. Fields, 2002. | MR | Zbl

[15] P. Eichelsbacher, U. Schmock, Large deviations for products of empirical measures of dependent sequences, Markov Process. Related Fields 7 (2001) 435-468. | MR | Zbl

[16] S.N. Ethier, T.G. Kurtz, Markov Processes, Characterization and Convergence, John Wiley & Sons, New York, 1986. | MR | Zbl

[17] P. Gänssler, Compactness and sequential compactness in spaces of measures, Z. Wahrscheinlichkeitstheorie verw. Geb. 17 (1971) 124-146. | MR | Zbl

[18] P. Groeneboom, J. Oosterhoff, F.H. Ruymgaart, Large deviation theorems for empirical probability measures, Ann. Probab. 7 (1979) 553-586. | MR | Zbl

[19] J.L. Kelley, General Topology, D. Van Nostrand, New York, 1955. | MR | Zbl

[20] A.J. Lee, U-Statistics: Theory and Practice, Marcel Dekker, New York, 1990. | MR | Zbl

[21] M. Löwe, Exponential inequalities and principles of large deviations for U-statistics and von Mises-statistics, Ph.D. thesis, Universität Bielefeld, Germany, 1992. | Zbl

[22] J. Neveu, Discrete-Parameter Martingales, North-Holland, Amsterdam, 1975. | MR | Zbl

[23] I.N. Sanov, On the probability of large deviations of random variables, Selected Transl. Math. Statist. and Prob. I (1961) 214-244. | MR | Zbl

[24] A. Schied, Große Abweichungen für die Pfade der Super-Brownschen Bewegung, Ph.D. thesis, Universität Bonn, Germany, 1994.

[25] A. Schied, Cramér's condition and Sanov's theorem, Statist. Probab. Lett. 39 (1) (1998) 55-60. | MR | Zbl

[26] U. Schmock, On the maximum entropy principle for Markov chains and processes, Ph.D. thesis, Technische Universität Berlin, Germany, 1990. | Zbl

[27] L. Wu, Some general methods of large deviations and applications, Preprint, 1993.