A limit theorem related to a new class of self similar processes

Summary We study partial sums of a stationary sequence of dependent random variables of the form . Here S _k =X ₁ + ... +X _k where the X _i are i.i.d. integer valued, and (n), n are also i.i.d. and independent of the X's. It is assumed that the X's and 's belong to the domains of attraction of different stable laws of indices 1<2 and 0<2. It is shown that for some > , n ^– W _nt] converges weakly as n to a self similar process with stationary increments, which depends on and . The constant is related to and via =1– ^–1+()^–1.Supported by the NSF at Cornell UniversityTo Leo Schmetterer on his 60^th anniversary