Doob: A Half-Century on

Abstract

Probability theory, and its dynamic aspect stochastic process theory, is both a venerable subject, in that its roots go back to the mid-seventeenth century, and a young one, in that its modern formulation happened comparatively recently - well within living memory. The year 2003 marked the seventieth anniversary of Kolmogorov'sGrundbegriffe der Wahrscheinlichkeitsrechnung, usually regarded as having inaugurated modern (measure-theoretic) probability theory. It also marked the fiftieth anniversary of Doob'sStochastic Processes. The profound and continuing influence of this classic work prompts the present piece.