Asymptotic results for hybrids of empirical and partial sums processes

The present paper is devoted to the study of the hybrids of empirical and partial sums processes. In the first part, we present a synthesis of results related to these processes and their connection with the empirical and compound process. We obtain new results on the precise asymptotics in the law of the logarithm related to complete convergence and a.s. convergence, under some mild conditions, for the hybrids of empirical and partial sums processes. Finally, the weighted bootstrap processes and general hybrid processes are also discussed.