J. L. Doob (27 February 1910--7 June 2004)

TL;DR

This paper reviews J. L. Doob's fundamental contributions to probability theory, including martingale theory, the $h$-transform, and his influential books, highlighting the evolution of his ideas over time.

Contribution

It provides a comprehensive overview of Doob's key results and their impact on stochastic analysis, especially in light of developments in the 1980s.

Findings

Doob's martingale theory laid foundational principles for modern probability.

The $h$-transform advanced the understanding of conditioned stochastic processes.

Doob's 'stochastic triangle' connects core concepts in stochastic analysis.

Abstract

Doob's essential contributions to Probability theory are discussed; this includes the main early results on martingale theory, Doob's $h$-transform, as well as a summary of Doob's three books. Finally, Doob's `stochastic triangle' is viewed in the light of the stochastic analysis of the eighties.