Martingale theory is a cornerstone of modern probability, offering a natural extension of the study of sums of independent random variables [...]. This book provides a comprehensive treatment of both classical and advanced martingale theory.
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It opens with a historical introduction, exploring foundational functions such as Rademacher, Haar, and Walsh functions, before delving into the core concepts of conditional probability. The classical theory, as developed by Doob, is meticulously presented, followed by an in-depth examination of modern advancements, including Burkholder’s inequalities, Burkholder-Davis-Gundy inequality, and their generalizations, as well as good-lambda inequalities. The final chapter showcases a wide range of applications, highlighting the theory’s profound impact on Banach space theory, harmonic analysis, and beyond [...]. (Estratto dal sito dell'editore)
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An *introduction to the modern martingale theory and applications : an analytic view / Wilfredo Urbina-Romero, Ricardo Rios. - Cham : Springer, 2025. - 1 testo elettronico (xvi, 276 p. : ill.)
