Limit Theorems For Sequences of Tempered Stable and Related   Distributions
  In this paper we define the closure under weak convergence of the class of p-tempered {\alpha}-stable distributions. We give necessary and sufficient conditions for convergence of sequences in this class. Moreover, we show that any element in this class can be approximated by the distribution of a linear combination of elementary p-tempered {\alpha}-stable random variables. 
Michael Grabchak
math.PR