Ldp of Partial Sums U - Processes 3

The large deviations principle (LDP) is known to hold for U-statistics of real valued kernel functions of Polish space valued i. i. d. random variables, where moreover appropriate exponential tail conditions are assumed to hold. We prove that similar conditions suuce for the large deviations principle to carry over to the partial sums U-processes corresponding to the statistics. x1 Introduction For a sequence of R d-valued i. i. d. random variables X i and with a law of X i having a nite moment generating function, Varadhan 19] proved a LDP for the partial sums process S n (t) = 1 n nt] X i=1 X i ; t 2 0; 1]: Mogulskii 16] extended the result to other scalings and also accomodated moment generating functions, which are nite only in a neighbourhood of the origin. In 15] the case of X i which are real valued functions of a regular nite state Markov chain is treated. Schuette 18] analysed real valued, independent but not necessarily identical distributed X i under more restrictive conditions on the corresponding moment generating functions. Moreover Dembo and Zajic 4] proved an extension of Varadhan's result to cover the LDP for L n (t) = 1 n nt] X i=1 X i ; t 2 0; 1];