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

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.