Large deviations of U-empirical measures in strong topologies and applications

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1. [1] A. de Acosta, On large deviations of empirical measures in the τ-topology, J. Appl. Probab.31A (1994) 41-47, (special volume). Zbl0810.60022
2. [2] R. Azencott, Grandes Déviations et Applications, Lectures Notes in Mathematics, 774, Springer-Verlag, Berlin, 1980. Zbl0435.60028MR590626
3. [3] R.R. Bahadur, S.L. Zabell, Large deviations of the sample mean in general vector spaces, Ann. Probab.7 (1979) 587-621. Zbl0424.60028MR537209
4. [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. Zbl0306.05137MR416986
5. [5] Yu.V. Borovskikh, U-Statistics in Banach Spaces, VSP, Utrecht, 1996. Zbl0865.60004MR1419498
6. [6] S.D. Chatterji, Martingale convergence and the Radon–Nikodým theorem in Banach spaces, Math. Scand.22 (1) (1968) 21-41. Zbl0175.14503
7. [7] I. Csiszár, I-divergence geometry of probability distributions and minimization problems, Ann. Probab.3 (1) (1975) 146-158. Zbl0318.60013MR365798
8. [8] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, Springer-Verlag, New York, 1998. Zbl0896.60013MR1619036
9. [9] J.-D. Deuschel, D.W. Stroock, Large Deviations, Pure and Applied Mathematics, 137, Academic Press, San Diego, 1989. Zbl0705.60029MR997938
10. [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. Zbl0348.60032MR428471
11. [11] H. Dym, H.P. McKean, Fourier Series and Integrals, Academic Press, New York and London, 1972. Zbl0242.42001MR442564
12. [12] P. Eichelsbacher, Large deviations for products of empirical probability measures in the τ-topology, J. Theoret. Probab.10 (3) (1997) 903-929. Zbl0891.60031
13. [13] P. Eichelsbacher, M. Löwe, Large deviation principle for m-variate von Mises-statistics and U-statistics, J. Theoret. Probab.8 (1995) 807-824. Zbl0835.60019MR1353555
14. [14] P. Eichelsbacher, U. Schmock, Rank-dependent moderate deviations of U-empirical measures in strong topologies, submitted to Probab. Theor. Relat. Fields, 2002. Zbl1039.60023MR1981633
15. [15] P. Eichelsbacher, U. Schmock, Large deviations for products of empirical measures of dependent sequences, Markov Process. Related Fields7 (2001) 435-468. Zbl1002.60023MR1856491
16. [16] S.N. Ethier, T.G. Kurtz, Markov Processes, Characterization and Convergence, John Wiley & Sons, New York, 1986. Zbl0592.60049MR838085
17. [17] P. Gänssler, Compactness and sequential compactness in spaces of measures, Z. Wahrscheinlichkeitstheorie verw. Geb.17 (1971) 124-146. Zbl0202.04904MR283562
18. [18] P. Groeneboom, J. Oosterhoff, F.H. Ruymgaart, Large deviation theorems for empirical probability measures, Ann. Probab.7 (1979) 553-586. Zbl0425.60021MR537208
19. [19] J.L. Kelley, General Topology, D. Van Nostrand, New York, 1955. Zbl0066.16604MR70144
20. [20] A.J. Lee, U-Statistics: Theory and Practice, Marcel Dekker, New York, 1990. Zbl0771.62001MR1075417
21. [21] M. Löwe, Exponential inequalities and principles of large deviations for U-statistics and von Mises-statistics, Ph.D. thesis, Universität Bielefeld, Germany, 1992. Zbl0827.60018
22. [22] J. Neveu, Discrete-Parameter Martingales, North-Holland, Amsterdam, 1975. Zbl0345.60026MR402915
23. [23] I.N. Sanov, On the probability of large deviations of random variables, Selected Transl. Math. Statist. and Prob.I (1961) 214-244. Zbl0112.10106MR116378
24. [24] A. Schied, Große Abweichungen für die Pfade der Super-Brownschen Bewegung, Ph.D. thesis, Universität Bonn, Germany, 1994. 
25. [25] A. Schied, Cramér's condition and Sanov's theorem, Statist. Probab. Lett.39 (1) (1998) 55-60. Zbl0911.60019MR1649347
26. [26] U. Schmock, On the maximum entropy principle for Markov chains and processes, Ph.D. thesis, Technische Universität Berlin, Germany, 1990. Zbl0714.60020
27. [27] L. Wu, Some general methods of large deviations and applications, Preprint, 1993. 

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