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

Abstract

We study partial sums of a stationary sequence of dependent random variables of the form {Mathematical expression}. Here Sk=X1 + ... +Xk where the Xiare i.i.d. integer valued, and ξ(n), n∈ℤ are also i.i.d. and independent of the X's. It is assumed that the X's and ξ's belong to the domains of attraction of different stable laws of indices 1 {Mathematical expression}, n-δW[nt] converges weakly as n→∞ to a self similar process with stationary increments, which depends on α and β. The constant δ is related to α and β via δ=1-α-1+(αβ)-1. © 1979 Springer-Verlag.