S Minaire De Probabilit S Xliii

Provides a foundation for probability based on game theory rather than measure theory. A strong philosophical approach with practical applications. Presents in-depth coverage of classical probability theory as well as new theory.

This is a new volume of the Séminaire de Probabilités which is now in its 43rd year. Following the tradition, this volume contains about 20 original research and survey articles on topics related to stochastic analysis. It contains an advanced course of J. Picard on the representation formulae for fractional Brownian motion. The regular chapters cover a wide range of themes, such as stochastic calculus and stochastic differential equations, stochastic differential geometry, filtrations, analysis on Wiener space, random matrices and free probability, as well as mathematical finance. Some of the contributions were presented at the Journées de Probabilités held in Poitiers in June 2009.

Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Get comprehensive, practical coverage of both surgical and non-surgical treatment approaches from the world’s most trusted authorities in spine surgery and care. Rothman-Simeone and Herkowitz’s The Spine, 7th Edition, edited by Drs. Steven R. Garfin, Frank J. Eismont, Gordon R. Bell, Jeffrey S. Fischgrund, and Christopher M. Bono, presents state-of-the-art techniques helping you apply today’s newest developments in your practice. Highlights critical information through the use of pearls, pitfalls, and key points throughout the text, as well as more than 2,300 full-color photographs and illustrations. Offers a newly revised, streamlined format that makes it easier than ever to find the information you need. Contains new chapters on the clinical relevance of finite element modeling and SI joint surgery. Includes an expanded section on minimally invasive spine surgery, including recent developments and future directions. Provides the latest evidence-based research from high-quality studies, including new randomized controlled trials for lumbar stenosis, surgery, fusion, and injections. Presents the knowledge and expertise of new international contributors, as well as new editorial leadership from Dr. Steven Garfin.

This book focuses on applications of martingales to the geometry of Banach spaces, and is accessible to graduate students.