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Real and Functional Analysis
This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.
Topological Vector Spaces and Their Applications
This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. Overall, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.
Trends in Stochastic Analysis
Presenting important trends in the field of stochastic analysis, this collection of thirteen articles provides an overview of recent developments and new results. Written by leading experts in the field, the articles cover a wide range of topics, ranging from an alternative set-up of rigorous probability to the sampling of conditioned diffusions. Applications in physics and biology are treated, with discussion of Feynman formulas, intermittency of Anderson models and genetic inference. A large number of the articles are topical surveys of probabilistic tools such as chaining techniques, and of research fields within stochastic analysis, including stochastic dynamics and multifractal analysis. Showcasing the diversity of research activities in the field, this book is essential reading for any student or researcher looking for a guide to modern trends in stochastic analysis and neighbouring fields.
Dirichlet Forms and Stochastic Processes
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Elliptic Boundary Value Problems and Construction of Lp-Strong Feller Processes with Singular Drift and Reflection
Benedict Baur presents modern functional analytic methods for construction and analysis of Feller processes in general and diffusion processes in particular. Topics covered are: Construction of Lp-strong Feller processes using Dirichlet form methods, regularity for solutions of elliptic boundary value problems, construction of elliptic diffusions with singular drift and reflection, Skorokhod decomposition and applications to Mathematical Physics like finite particle systems with singular interaction. Emphasize is placed on the handling of singular drift coefficients, as well as on the discussion of point wise and path wise properties of the constructed processes rather than just the quasi-everywhere properties commonly known from the general Dirichlet form theory.
Quantum Bio-informatics V - Proceedings Of The Quantum Bio-informatics 2011
This volume is based on the fifth international conference of quantum bio-informatics held at the QBI Center of Tokyo University of Science.This volume provides a platform to connect mathematics, physics, information and life sciences, and in particular, research for new paradigm for information science and life science on the basis of quantum theory.The following topics are discussed:
New Trends in Stochastic Analysis and Related Topics
The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehe...
