Set-Indexed Martingales (eBook)

B.G. Ivanoff, Ely Merzbach (Autoren)

eBook Download: PDF

2024
224 Seiten
CRC Press (Verlag)
978-1-351-41681-8 (ISBN)

Infos

Set-Indexed Martingales offers a unique, comprehensive development of a general theory of Martingales indexed by a family of sets. The authors establish-for the first time-an appropriate framework that provides a suitable structure for a theory of Martingales with enough generality to include many interesting examples. Developed from first principles, the theory brings together the theories of Martingales with a directed index set and set-indexed stochastic processes. Part One presents several classical concepts extended to this setting, including: stopping, predictability, Doob-Meyer decompositions, martingale characterizations of the set-indexed Poisson process, and Brownian motion. Part Two addresses convergence of sequences of set-indexed processes and introduces functional convergence for processes whose sample paths live in a Skorokhod-type space and semi-functional convergence for processes whose sample paths may be badly behaved.Completely self-contained, the theoretical aspects of this work are rich and promising. With its many important applications-especially in the theory of spatial statistics and in stochastic geometry- Set Indexed Martingales will undoubtedly generate great interest and inspire further research and development of the theory and applications.

Produkt-Details

• Erscheint lt. Verlag: 15.12.2024
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• ISBN-10: 1-351-41681-2 / 1351416812
• ISBN-13: 978-1-351-41681-8 / 9781351416818