Ricardo Rios – författare

This book highlights recent research on bio-inspired computing and its various innovative applications in information and communication technologies. It presents 51 high-quality papers from the 11th International Conference on Innovations in Bio-Inspired Computing and Applications (IBICA 2020) and 10th World Congress on Information and Communication Technologies (WICT 2020), which was held online during December 16–18, 2019. As a premier conference, IBICA–WICT brings together researchers, engineers and practitioners whose work involves bio-inspired computing, computational intelligence and their applications in information security, real-world contexts, etc. Including contributions by authors from 25 countries, the book offers a valuable reference guide for all researchers, students and practitioners in the fields of Computer Science and Engineering.

This book highlights recent research on bio-inspired computing and its various innovative applications in information and communication technologies. It presents 51 high-quality papers from the 11th International Conference on Innovations in Bio-Inspired Computing and Applications (IBICA 2020) and 10th World Congress on Information and Communication Technologies (WICT 2020), which was held online during December 16–18, 2019. As a premier conference, IBICA–WICT brings together researchers, engineers and practitioners whose work involves bio-inspired computing, computational intelligence and their applications in information security, real-world contexts, etc. Including contributions by authors from 25 countries, the book offers a valuable reference guide for all researchers, students and practitioners in the fields of Computer Science and Engineering.

Martingale theory is a cornerstone of modern probability, offering a natural extension of the study of sums of independent random variables. Although its roots can be traced back to the work of Paul Lévy in 1937, it was Joseph L. Doob in the 1940s who formally developed the theory, culminating in his landmark book Stochastic Processes in 1953. Since then, martingale theory has evolved significantly, with deep contributions from mathematicians such as Donald L. Burkholder, Richard Gundy, and Burgess Davis, among others. This is what is now known as advanced martingale theory, which began with the publication of Burkholder’s seminal paper Martingale Transforms in 1966.This book provides a comprehensive treatment of both classical and advanced martingale theory. 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.Intended for graduate students and researchers in probability and analysis, this book serves as both an introduction and a reference, offering a clear and structured approach to a subject that continues to shape mathematical research and its applications.