@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://www.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://www.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://www.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://www.numdam.org/item/AIHPB_2002__38_5_779_0/
[1] On large deviations of empirical measures in the τ-topology, J. Appl. Probab. 31A (1994) 41-47, (special volume). | Zbl
,[2] Grandes Déviations et Applications, Lectures Notes in Mathematics, 774, Springer-Verlag, Berlin, 1980. | MR | Zbl
,[3] Large deviations of the sample mean in general vector spaces, Ann. Probab. 7 (1979) 587-621. | MR | Zbl
, ,[4] On the factorisation of the complete uniform hypergraph, in: , , (Eds.), Infinite and Finite Sets, North-Holland, Amsterdam, 1975, pp. 91-108. | MR | Zbl
,[5] U-Statistics in Banach Spaces, VSP, Utrecht, 1996. | MR | Zbl
,[6] Martingale convergence and the Radon-Nikodým theorem in Banach spaces, Math. Scand. 22 (1) (1968) 21-41. | Zbl
,[7] I-divergence geometry of probability distributions and minimization problems, Ann. Probab. 3 (1) (1975) 146-158. | MR | Zbl
,[8] Large Deviations Techniques and Applications, Springer-Verlag, New York, 1998. | MR | Zbl
, ,[9] Large Deviations, Pure and Applied Mathematics, 137, Academic Press, San Diego, 1989. | MR | Zbl
, ,[10] Asymptotic evaluation of certain Markov process expectations for large time III, Comm. Pure Appl. Math. 29 (1976) 389-461. | MR | Zbl
, ,[11] Fourier Series and Integrals, Academic Press, New York and London, 1972. | MR | Zbl
, ,[12] Large deviations for products of empirical probability measures in the τ-topology, J. Theoret. Probab. 10 (3) (1997) 903-929. | Zbl
,[13] 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] Large deviations for products of empirical measures of dependent sequences, Markov Process. Related Fields 7 (2001) 435-468. | MR | Zbl
, ,[16] Markov Processes, Characterization and Convergence, John Wiley & Sons, New York, 1986. | MR | Zbl
, ,[17] Compactness and sequential compactness in spaces of measures, Z. Wahrscheinlichkeitstheorie verw. Geb. 17 (1971) 124-146. | MR | Zbl
,[18] Large deviation theorems for empirical probability measures, Ann. Probab. 7 (1979) 553-586. | MR | Zbl
, , ,[19] General Topology, D. Van Nostrand, New York, 1955. | MR | Zbl
,[20] U-Statistics: Theory and Practice, Marcel Dekker, New York, 1990. | MR | Zbl
,[21] Exponential inequalities and principles of large deviations for U-statistics and von Mises-statistics, Ph.D. thesis, Universität Bielefeld, Germany, 1992. | Zbl
,[22] Discrete-Parameter Martingales, North-Holland, Amsterdam, 1975. | MR | Zbl
,[23] On the probability of large deviations of random variables, Selected Transl. Math. Statist. and Prob. I (1961) 214-244. | MR | Zbl
,[24] Große Abweichungen für die Pfade der Super-Brownschen Bewegung, Ph.D. thesis, Universität Bonn, Germany, 1994.
,[25] Cramér's condition and Sanov's theorem, Statist. Probab. Lett. 39 (1) (1998) 55-60. | MR | Zbl
,[26] On the maximum entropy principle for Markov chains and processes, Ph.D. thesis, Technische Universität Berlin, Germany, 1990. | Zbl
,[27] Some general methods of large deviations and applications, Preprint, 1993.
,