Geodesic
Large deviations for partial sums $U$-processes in dependent cases
Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 4, pp. 670-693 Cet article a éte moissonné depuis la source Math-Net.Ru

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The large deviation principle (LDP) is known to hold for partial sums $U$-processes of real-valued kernel functions of independent identically distributed random variables $X_i$. We prove an LDP when the $X_i$ are independent but not identically distributed or fulfill some Markov dependence or mixing conditions. Moreover, we give a general condition which suffices for the LDP to carry over from the partial sums empirical processes LDP to the partial sums $U$-processes LDP for kernel functions satisfying an appropriate exponential tail condition.
Keywords: large deviations, partial sums, $U$-process, strong mixing.
Mots-clés : Markov chains, hypermixing 
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     author = {P. Eichelsbacher},
     title = {Large deviations for partial sums $U$-processes in dependent cases},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {670--693},
     year = {2000},
     volume = {45},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2000_45_4_a3/}
}
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P. Eichelsbacher. Large deviations for partial sums $U$-processes in dependent cases. Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 4, pp. 670-693. http://geodesic.mathdoc.fr/item/TVP_2000_45_4_a3/