Large deviations of U-empirical measures in strong topologies and applications
Annales de l'I.H.P. Probabilités et statistiques, Volume 38 (2002) no. 5, p. 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},
     publisher = {Elsevier},
     volume = {38},
     number = {5},
     year = {2002},
     pages = {779-797},
     zbl = {1033.60033},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 38 (2002) no. 5, pp. 779-797. http://www.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 0810.60022

[2] R. Azencott, Grandes Déviations et Applications, Lectures Notes in Mathematics, 774, Springer-Verlag, Berlin, 1980. | MR 590626 | Zbl 0435.60028

[3] R.R. Bahadur, S.L. Zabell, Large deviations of the sample mean in general vector spaces, Ann. Probab. 7 (1979) 587-621. | MR 537209 | Zbl 0424.60028

[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 416986 | Zbl 0306.05137

[5] Yu.V. Borovskikh, U-Statistics in Banach Spaces, VSP, Utrecht, 1996. | MR 1419498 | Zbl 0865.60004

[6] S.D. Chatterji, Martingale convergence and the Radon-Nikodým theorem in Banach spaces, Math. Scand. 22 (1) (1968) 21-41. | Zbl 0175.14503

[7] I. Csiszár, I-divergence geometry of probability distributions and minimization problems, Ann. Probab. 3 (1) (1975) 146-158. | MR 365798 | Zbl 0318.60013

[8] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, Springer-Verlag, New York, 1998. | MR 1619036 | Zbl 0896.60013

[9] J.-D. Deuschel, D.W. Stroock, Large Deviations, Pure and Applied Mathematics, 137, Academic Press, San Diego, 1989. | MR 997938 | Zbl 0705.60029

[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 428471 | Zbl 0348.60032

[11] H. Dym, H.P. Mckean, Fourier Series and Integrals, Academic Press, New York and London, 1972. | MR 442564 | Zbl 0242.42001

[12] P. Eichelsbacher, Large deviations for products of empirical probability measures in the τ-topology, J. Theoret. Probab. 10 (3) (1997) 903-929. | Zbl 0891.60031

[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 1353555 | Zbl 0835.60019

[14] P. Eichelsbacher, U. Schmock, Rank-dependent moderate deviations of U-empirical measures in strong topologies, submitted to Probab. Theor. Relat. Fields, 2002. | MR 1981633 | Zbl 1039.60023

[15] P. Eichelsbacher, U. Schmock, Large deviations for products of empirical measures of dependent sequences, Markov Process. Related Fields 7 (2001) 435-468. | MR 1856491 | Zbl 1002.60023

[16] S.N. Ethier, T.G. Kurtz, Markov Processes, Characterization and Convergence, John Wiley & Sons, New York, 1986. | MR 838085 | Zbl 0592.60049

[17] P. Gänssler, Compactness and sequential compactness in spaces of measures, Z. Wahrscheinlichkeitstheorie verw. Geb. 17 (1971) 124-146. | MR 283562 | Zbl 0202.04904

[18] P. Groeneboom, J. Oosterhoff, F.H. Ruymgaart, Large deviation theorems for empirical probability measures, Ann. Probab. 7 (1979) 553-586. | MR 537208 | Zbl 0425.60021

[19] J.L. Kelley, General Topology, D. Van Nostrand, New York, 1955. | MR 70144 | Zbl 0066.16604

[20] A.J. Lee, U-Statistics: Theory and Practice, Marcel Dekker, New York, 1990. | MR 1075417 | Zbl 0771.62001

[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 0827.60018

[22] J. Neveu, Discrete-Parameter Martingales, North-Holland, Amsterdam, 1975. | MR 402915 | Zbl 0345.60026

[23] I.N. Sanov, On the probability of large deviations of random variables, Selected Transl. Math. Statist. and Prob. I (1961) 214-244. | MR 116378 | Zbl 0112.10106

[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 1649347 | Zbl 0911.60019

[26] U. Schmock, On the maximum entropy principle for Markov chains and processes, Ph.D. thesis, Technische Universität Berlin, Germany, 1990. | Zbl 0714.60020

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