Routledge Set-Indexed Martingales: Chapman & Hall Monograph 85

Set-Indexed Martingales presents a comprehensive and rigorous development of martingale theory indexed by families of sets, establishing a unified mathematical framework that integrates classical martingale concepts with set-indexed stochastic processes. Written by leading researchers and published as volume 85 in the Chapman and Hall/CRC Monographs on Statistics and Applied Probability series, this monograph develops the theory from first principles and extends foundational concepts including stopping, predictability, and Doob-Meyer decomposition to this generalised setting. The work addresses a significant gap in the literature by providing sufficient generality to encompass numerous important applications whilst maintaining rigorous mathematical treatment. Ideal for researchers, graduate students, and practitioners in probability theory, stochastic processes, and applied statistics, this text serves as both an advanced reference and a foundation for further investigation into set-indexed martingale theory and its applications across mathematical sciences and engineering disciplines.