The martingale method: Introductory sketch and access to the literature

Abstract

Since 1975 there has developed a powerful and sophisticated theory of statistical inference for point processes known as the ‘martingale method’. Because it is based on deep and in many cases technical results in the (French) general theory of stochastic processes, it has remained inaccessible to many who might usefully apply it. Yet the fundamental ideas (as opposed to the details, which can be formidable) are not hopelessly arcane; our purposes here are to describe the theory in a manner that reveals its underlying conceptual simplicity (although oversimplified, (6) below is the essential idea), to illustrate it with three examples, and to give some points of entry into the complex and now rather extensive literature. This is not a guide to application, much less even an incomplete development of the theory, but merely (so to speak) a silhoutte.