The origins of Skorokhod's topology (Q2726252)

For probability theory on the space of continuous functions on the unit interval there is a completely natural topology given by the uniform metric. Although this provides the appropriate setting for studying convergence of stochastic processes with continuous sample paths, it is entirely unsuitable for processes with paths that may contain jumps. Just over forty five years ago, in 1956, A. V. Skorokhod gave us a topology perfectly adapted to the analysis of convergence for processes of this kind. This paper gives a brief account of the early evolution of Skorokhod's idea. In these first papers different writers used slightly differing definitions and conventions (about jump discontinuities, for example), these authors made them uniform (all our functions are càdlàg, for example). As the authors write, ``this is a small history of a large idea''.NEWLINENEWLINEFor the entire collection see [Zbl 0956.00022].