Routledge Set-Indexed Martingales - Chapman & Hall/CRC Monographs

Set-Indexed Martingales provides a comprehensive development of a general theory for Martingales indexed by a family of sets. As part of the Chapman & Hall/CRC Monographs on Statistics and Applied Probability, this text establishes a new framework that offers enough generality to include many important examples. Developed from first principles, the theory combines the concepts of Martingales with a directed index set and set-indexed stochastic processes. This approach creates a unified structure for researchers and students in the fields of statistics and applied probability. Part One of the book extends several classical concepts to this new setting. Readers will find detailed coverage of essential topics including stopping, predictability, and Doob-Meyer decomposition. This monograph serves as a foundational resource for understanding advanced stochastic processes through a unique and rigorous lens.