The theory of semigroups of operators is a topic with great intellectual beauty and wide-ranging applications. This graduate-level introduction presents the essential elements of the theory, introducing the key notions and establishing the central theorems. A mixture of applications are included and further development directions are indicated.
This updated edition offers a comprehensive introduction to probability theory and information theory, now enhanced with new insights into Markov chains. It caters to both beginners and those looking to deepen their understanding, making complex concepts accessible. The inclusion of contemporary examples and applications ensures relevance in today's data-driven world, providing readers with a solid foundation in these essential mathematical fields.
The book presents a comprehensive exploration of Lévy processes and their relationship with stochastic calculus, emphasizing their applications in various fields like physics and finance. It introduces the general theory of Lévy processes and develops stochastic calculus tailored for them. The revised edition includes new topics such as regular variation, conditions for finite moments, and characterizations of Lévy processes. Additionally, it covers Kunita's estimates, new proofs of key theorems, multiple Wiener-Lévy integrals, Malliavin calculus, and stability theory for Lévy-driven stochastic differential equations.
Focusing on the intersection of chance and symmetry, this book offers a thorough introduction to probability theory on compact Lie groups. It covers essential topics such as non-commutative Fourier transforms, measure properties, random walks, and deconvolution challenges. By concentrating on compact Lie groups, the author makes this complex field more accessible, highlighting its relevance and applications in statistics and engineering, especially in signal processing. The text balances theoretical insights with practical applicability, making it a valuable resource for both students and professionals.
An account of elementary real analysis positioned between a popular mathematics book and a first year college or university text. This book doesn't assume knowledge of calculus and, instead, the emphasis is on the application of analysis to number theory.
This volume is the first of two volumes containing the revised and completed notes lectures given at the school „Quantum Independent Increment Processes: Structure and Applications to Physics“. This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald during the period March 9 – 22, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics. The present first volume contains the following lectures: „Lévy Processes in Euclidean Spaces and Groups“ by David Applebaum, „Locally Compact Quantum Groups“ by Johan Kustermans, „Quantum Stochastic Analysis“ by J. Martin Lindsay, and „Dilations, Cocycles and Product Systems“ by B. V. Rajarama Bhat.