| In this thesis we study weak limit theorems for sums and products of noncommutative random variables in an infinitesimal triangular array. We find necessary and suffcient conditions for weak convergence, and further use these limit theorems to investigate infinite divisibility relative to the corresponding convolution. We show that infinitely divisible laws arise as the limit laws for infinitesimal arrays, and they can be embedded into weakly continuous convolution semigroups as in the classical case. These results are proved by complex analytic methods. |
