In the random walk whose state space is a subset of the non-negative integers explicit representations for the generating functions of the n-step transition and the first return probabilities are ...

Leo A. Aroian, The Probability Function of the Product of Two Normally Distributed Variables, The Annals of Mathematical Statistics, Vol. 18, No. 2 (Jun., 1947), pp. 265-271 ...

Operator methods in probability: generating functions, moment generating functions, Laplace transforms, and characteristic functions. Notions of convergence: convergence in probability and weak laws ...