STRASSEN LIL FOR THE LORENZ CURVE

We prove Strassen's law of the iterated logarithm for the Lorenz proce ss assuming that the underlying distribution Function F and its invers e F-1 are continuous, and the moment EX(2+epsilon) is finite for some epsilon>0. Previous work in this area is based on assuming the existen ce of the density f:= F' combined with Further assumptions on F and f: Being based only on continuity and moment assumptions, our method of proof is different from that used previously by others, and is mainly based on a limit theorem for the (general) integrated empirical differ ence process. The obtained result covers all those we are aware of on the LIL problem in this area. (C) 1996 Academic Press, Inc.