As Ethier and Kurtz tell us in their preface, their original aims were to treat the general problem of weak convergence of a sequence of Markov processes to a Markov limit. Such problems are not only not new, but are classical. Who does not know of the convergence of a random walk to Brownian motion (as the number of steps becomes infinite and time and space are appropriately normalized) or of continuous-time diffusion
approximations to branching-type processes in discrete time? Not only are these results themselves now classical, but so were the majority of the techniques (most of which were not terribly elegant) that were originally used in their derivation. In recent years, however, this rather stable area of stochastic process theory has undergone a dramatic facelift, in view of substantial progress in both the areas of Markov processes and weak convergence. This book is an excellent account of this progress, told by authors who themselves have contributed significantly to its development.