  Let (W_i, J_i) be a sequence of i.i.d. R_+ x R-valued random vectors.
Considering the partial sum of the first component and the corresponding
maximum of the second component, we are interested in the limit distributions
that can be obtained under an appropriate scaling. In the case that W_i and J_i
are independent, the joint distribution of the sum and the maximum is the
product measure of the limit distributions of the two components. But if we
allow dependence between the two components, this dependence can still appear
in the limit, and we need a new theory to describe the possible limit
distributions. This is achieved via harmonic analysis on semigroups, which can
be utilized to characterize the scaling limit distributions and describe their
domains of attraction.
