Weak convergence in applied probability

AbstractWeak convergence of probability measures on function spaces has been active area of research in recent years. While the theory has a somewhat abstract base, it is extremely useful in a wide variety of problems and we believe has much to offer to applied probability. Our aim in this survey paper is to discuss those aspects of the theory which are relevant to work in applied probability. After an introduction to the foundations of weak convergence, we shall discuss partial sum, point, Markov and extremal processes. These processes form the building blocks for many of the important models of applied probability