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White Noise On Bialgebras
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Book Synopsis White Noise on Bialgebras by : Michael Schürmann
Download or read book White Noise on Bialgebras written by Michael Schürmann and published by Springer. This book was released on 2006-11-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic processes with independent increments on a group are generalized to the concept of "white noise" on a Hopf algebra or bialgebra. The main purpose of the book is the characterization of these processes as solutions of quantum stochastic differential equations in the sense of R.L. Hudsonand K.R. Parthasarathy. The notes are a contribution to quantum probability but they are also related to classical probability, quantum groups, and operator algebras. The Az ma martingales appear as examples of white noise on a Hopf algebra which is a deformation of the Heisenberg group. The book will be of interest to probabilists and quantum probabilists. Specialists in algebraic structures who are curious about the role of their concepts in probablility theory as well as quantum theory may find the book interesting. The reader should havesome knowledge of functional analysis, operator algebras, and probability theory.
Book Synopsis Stochastic Processes and Operator Calculus on Quantum Groups by : U. Franz
Download or read book Stochastic Processes and Operator Calculus on Quantum Groups written by U. Franz and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present several new developments on stochastic processes and operator calculus on quantum groups. Topics which are treated include operator calculus, dual representations, stochastic processes and diffusions, Appell polynomials and systems in connection with evolution equations. Audience: This volume contains introductory material for graduate students who are new to the field, as well as more advanced material for specialists in probability theory, algebraic structures, representation theory, mathematical physics and theoretical physics.
Book Synopsis Quantum Stochastics and Information by : V. P. Belavkin
Download or read book Quantum Stochastics and Information written by V. P. Belavkin and published by World Scientific. This book was released on 2008 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum stochastic calculus has become an indispensable tool in modern quantum physics, its effectiveness being illustrated by recent developments in quantum control which place the calculus at the heart of the theory. Quantum statistics is rapidly taking shape as an intrinsically quantum counterpart to classical statistics, motivated by advances in quantum engineering and the need for better statistical inference tools for quantum systems.This volume contains a selection of regular research articles and reviews by leading researchers in quantum control, quantum statistics, quantum probability and quantum information. The selection offers a unified view of recent trends in quantum stochastics, highlighting the common mathematical language of Hilbert space operators, and the deep connections between classical and quantum stochastic phenomena.
Book Synopsis Noncommutative Probability by : I. Cuculescu
Download or read book Noncommutative Probability written by I. Cuculescu and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of this book is to explain to a mathematician having no previous knowledge in this domain, what "noncommutative probability" is. So the first decision was not to concentrate on a special topic. For different people, the starting points of such a domain may be different. In what concerns this question, different variants are not discussed. One such variant comes from Quantum Physics. The motivations in this book are mainly mathematical; more precisely, they correspond to the desire of developing a probability theory in a new set-up and obtaining results analogous to the classical ones for the newly defined mathematical objects. Also different mathematical foundations of this domain were proposed. This book concentrates on one variant, which may be described as "von Neumann algebras". This is true also for the last chapter, if one looks at its ultimate aim. In the references there are some papers corresponding to other variants; we mention Gudder, S.P. &al (1978). Segal, I.E. (1965) also discusses "basic ideas".
Book Synopsis Quantum Probability and Related Topics by : Rolando Rebolledo
Download or read book Quantum Probability and Related Topics written by Rolando Rebolledo and published by World Scientific. This book was released on 2011 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains current work at the frontiers of research in quantum probability, infinite dimensional stochastic analysis, quantum information and statistics. It presents a carefully chosen collection of articles by experts to highlight the latest developments in those fields. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.
Book Synopsis Quantum Probability And Related Topics - Proceedings Of The 30th Conference by : Rolando Rebolledo
Download or read book Quantum Probability And Related Topics - Proceedings Of The 30th Conference written by Rolando Rebolledo and published by World Scientific. This book was released on 2011-01-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains current work at the frontiers of research in quantum probability, infinite dimensional stochastic analysis, quantum information and statistics. It presents a carefully chosen collection of articles by experts to highlight the latest developments in those fields. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.
Book Synopsis Quantum Probability Communications by : R. L. Hudson
Download or read book Quantum Probability Communications written by R. L. Hudson and published by World Scientific. This book was released on 1998 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much has changed in the world of quantum probability since the publication of the last volume in this series. Giants in the field, such as P-A Meyer, K R Parthasarathy and W von Waldenfels, have reached the age of retirement. Readers will, however, be pleased to see evidence in the present volume that Partha remains as creatively active as ever. The field itself, regarded at one time as the esoteric province of a small group of devotees, has come of age. It has attracted the enthusiastic commitment of an ever-growing army of young mathematicians and physicists, many of whom are represented here.
Book Synopsis Combinatorial Theory of the Free Product with Amalgamation and Operator-Valued Free Probability Theory by : Roland Speicher
Download or read book Combinatorial Theory of the Free Product with Amalgamation and Operator-Valued Free Probability Theory written by Roland Speicher and published by American Mathematical Soc.. This book was released on 1998 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Free probability theory, introduced by Voiculescu, has developed very actively in the last few years and has had an increasing impact on quite different fields in mathematics and physics. Whereas the subject arose out of the field of von Neumann algebras, presented here is a quite different view of Voiculescu's amalgamated free product. This combinatorial description not only allows re-proving of most of Voiculescu's results in a concise and elegant way, but also opens the way for many new results. Unlike other approaches, this book emphasizes the combinatorial structure of the concept of ``freeness''. This gives an elegant and easily accessible description of freeness and leads to new results in unexpected directions. Specifically, a mathematical framework for otherwise quite ad hoc approximations in physics emerges.
Book Synopsis Noncommutative Mathematics for Quantum Systems by : Uwe Franz
Download or read book Noncommutative Mathematics for Quantum Systems written by Uwe Franz and published by Cambridge University Press. This book was released on 2016-01-07 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known 'commutative' results. On the other hand the richness of the quantum mathematical world presents completely novel phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physics and operator algebras.
Book Synopsis Quantum Probability And Infinite Dimensional Analysis: From Foundations To Appllications by : Uwe Franz
Download or read book Quantum Probability And Infinite Dimensional Analysis: From Foundations To Appllications written by Uwe Franz and published by World Scientific. This book was released on 2005-01-12 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects research papers in quantum probability and related fields and reflects the recent developments in quantum probability ranging from the foundations to its applications.
Book Synopsis Recent Developments In Stochastic Analysis And Related Topics - Proceedings Of The First Sino-german Conf On Stochastic Analysis (A Satellite Conference Of Icm 2002) by : Sergio Albeverio
Download or read book Recent Developments In Stochastic Analysis And Related Topics - Proceedings Of The First Sino-german Conf On Stochastic Analysis (A Satellite Conference Of Icm 2002) written by Sergio Albeverio and published by World Scientific. This book was released on 2004-10-21 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 27 refereed research articles and survey papers written by experts in the field of stochastic analysis and related topics. Most contributors are well known leading mathematicians worldwide and prominent young scientists. The volume reflects a review of the recent developments in stochastic analysis and related topics. It puts in evidence the strong interconnection of stochastic analysis with other areas of mathematics, as well as with applications of mathematics in natural and social economic sciences. The volume also provides some possible future directions for the field.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
Book Synopsis Equivariant Sheaves and Functors by : Joseph Bernstein
Download or read book Equivariant Sheaves and Functors written by Joseph Bernstein and published by Springer. This book was released on 2006-11-15 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: The equivariant derived category of sheaves is introduced. All usual functors on sheaves are extended to the equivariant situation. Some applications to the equivariant intersection cohomology are given. The theory may be useful to specialists in representation theory, algebraic geometry or topology.
Book Synopsis Extrapolation and Optimal Decompositions by : Mario Milman
Download or read book Extrapolation and Optimal Decompositions written by Mario Milman and published by Springer. This book was released on 2006-11-15 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a theory of extrapolation spaces with applications to classical and modern analysis. Extrapolation theory aims to provide a general framework to study limiting estimates in analysis. The book also considers the role that optimal decompositions play in limiting inequalities incl. commutator estimates. Most of the results presented are new or have not appeared in book form before. A special feature of the book are the applications to other areas of analysis. Among them Sobolev imbedding theorems in different contexts including logarithmic Sobolev inequalities are obtained, commutator estimates are connected to the theory of comp. compactness, a connection with maximal regularity for abstract parabolic equations is shown, sharp estimates for maximal operators in classical Fourier analysis are derived.
Book Synopsis From Divergent Power Series to Analytic Functions by : Werner Balser
Download or read book From Divergent Power Series to Analytic Functions written by Werner Balser and published by Springer. This book was released on 2006-11-15 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.
Book Synopsis Lectures on Probability Theory by : Dominique Bakry
Download or read book Lectures on Probability Theory written by Dominique Bakry and published by Springer. This book was released on 2006-11-15 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains work-outs of the notes of three 15-hour courses of lectures which constitute surveys on the concerned topics given at the St. Flour Probability Summer School in July 1992. The first course, by D. Bakry, is concerned with hypercontractivity properties and their use in semi-group theory, namely Sobolev and Log Sobolev inequa- lities, with estimations on the density of the semi-groups. The second one, by R.D. Gill, is about statistics on survi- val analysis; it includes product-integral theory, Kaplan- Meier estimators, and a look at cryptography and generation of randomness. The third one, by S.A. Molchanov, covers three aspects of random media: homogenization theory, loca- lization properties and intermittency. Each of these chap- ters provides an introduction to and survey of its subject.
Book Synopsis The Boundary-Domain Integral Method for Elliptic Systems by : Andreas Pomp
Download or read book The Boundary-Domain Integral Method for Elliptic Systems written by Andreas Pomp and published by Springer Science & Business Media. This book was released on 1998-03-18 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives a description of all algorithmic steps and a mathematical foundation for a special numerical method, namely the boundary-domain integral method (BDIM). This method is a generalization of the well-known boundary element method, but it is also applicable to linear elliptic systems with variable coefficients, especially to shell equations. The text should be understandable at the beginning graduate-level. It is addressed to researchers in the fields of numerical analysis and computational mechanics, and will be of interest to everyone looking at serious alternatives to the well-established finite element methods.
Book Synopsis Séminaire de Probabilités XXXII by : Jacques Azema
Download or read book Séminaire de Probabilités XXXII written by Jacques Azema and published by Springer. This book was released on 2007-01-05 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: All the papers in the volume are original research papers, discussing fundamental properties of stochastic processes. The topics under study (martingales, filtrations, path properties, etc.) represent an important part of the current research performed in 1996-97 by various groups of probabilists in France and abroad.