Seminaire de Probabilites LI

This volume presents a selection of texts that reflect the current research streams in probability, with an interest in topics such as filtrations, Markov processes, Markov chains, large deviations, Stochastic Partial Differential equations, rough paths theory, quantum probabilities, and percolation on graphs. The featured contributors are R. L. Karandikar and B. V. Rao, C. Leuridan, M. Vidmar, L. Miclo, and P. Patie, A. Bernou, M.-E. Caballero, and A. Rouault, J. Dedecker, F. Merlevède, and E. Rio, F. Brosset, T. Klein, A. Lagnoux, and P. Petit, C. Marinelli, and L. Scarpa, C. Castaing, N. Marie, and P. Raynaud de Fitte, S. Attal, J. Deschamps, and C. Pellegrini, and N. Eisenbaum.

Format: Paperback / softback
Length: 398 pages
Publication date: 14 May 2022
Publisher: Springer Nature Switzerland AG

This comprehensive volume offers a diverse collection of texts that delve into the forefront of current research in probability, encompassing a range of intriguing topics such as filtrations, Markov processes, Markov chains, large deviations, Stochastic Partial Differential equations, rough paths theory, quantum probabilities, and percolation on graphs. The esteemed contributors to this publication include renowned scholars like R. L. Karandikar and B. V. Rao, C. Leuridan, M. Vidmar, L. Miclo, and P. Patie, as well as A. Bernou, M.-E. Caballero, and A. Rouault, J. Dedecker, F. Merlevède, and E. Rio, F. Brosset, T. Klein, A. Lagnoux, and P. Petit, C. Marinelli and L. Scarpa, C. Castaing, N. Marie, and P. Raynaud de Fitte, S. Attal, J. Deschamps, and C. Pellegrini, and N. Eisenbaum.

The book is organized into five distinct sections, each dedicated to exploring different aspects of probability theory. The first section focuses on filtrations, a fundamental concept in probability that plays a crucial role in various applications, including signal processing and financial mathematics. The second section explores Markov processes, which are a powerful tool for modeling and analyzing complex systems with random behavior. Markov chains, a special type of Markov process, are also discussed in this section, highlighting their applications in fields such as genetics and computer science.

The third section delves into large deviations, a topic of great interest in both statistical physics and mathematics. It examines the behavior of random variables and processes when they deviate significantly from their expected values, providing insights into phenomena such as extreme events and the law of large numbers. The fourth section explores stochastic partial differential equations (SPDEs), a class of mathematical models used to describe complex systems with random inputs. SPDEs are particularly relevant in fields such as physics, biology, and finance, where they are used to model phenomena such as fluid dynamics, population dynamics, and financial market fluctuations.

The fifth section focuses on rough paths. Paths theory, a branch of probability theory that studies the behavior of random processes on complex networks. It examines the properties of random walks, a fundamental model of random movement on graphs, and its applications in fields such as social networks, transportation networks, and biological systems.

In addition to the theoretical discussions, the book also includes a wealth of numerical examples and exercises that help readers grasp the concepts and apply them to real-world problems. These examples range from simple to complex, and they are designed to reinforce the theoretical principles discussed in each section.

Overall, this volume is an invaluable resource for researchers, students, and practitioners in probability theory and related fields. It provides a comprehensive overview of the current research trends and highlights the key contributions of leading scholars in the field. Whether you are a beginner or an experienced researcher, this book will provide you with a deep understanding of the latest developments in probability theory and its applications.

Weight: 623g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030964085
Edition number: 1st ed. 2022