Large deviations for partial sums $U$-processes in dependent cases

P. Eichelsbacher

Fakultat für Mathematik, Universität Bielefeld, Germany

Abstract: 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, Markov chains, hypermixing, strong mixing.

Received: 26.06.1998

Language: English

DOI: 10.4213/tvp498

 English version: Theory of Probability and its Applications, 2001, 45:4, 569–588

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