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Author : Jörg-Uwe Löbus
Publisher : Wiley-VCH
ISBN 13 :
Total Pages : 122 pages
Book Rating : 4.F/5 ( download)
Download or read book Generalized Diffusion Operators written by Jörg-Uwe Löbus and published by Wiley-VCH. This book was released on 1993-09-15 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Nikola_ Ivanovich Portenko
Publisher : American Mathematical Soc.
ISBN 13 : 9780821898260
Total Pages : 200 pages
Book Rating : 4.8/5 (982 download)
Download or read book Generalized Diffusion Processes written by Nikola_ Ivanovich Portenko and published by American Mathematical Soc.. This book was released on 1990-12-21 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diffusion processes serve as a mathematical model for the physical phenomenon of diffusion. One of the most important problems in the theory of diffusion processes is the development of methods for constructing these processes from a given diffusion matrix and a given drift vector. Focusing on the investigation of this problem, this book is intended for specialists in the theory of random processes and its applications. A generalized diffusion process (that is, a continuous Markov process for which the Kolmogorov local characteristics exist in the generalized sense) can serve as a model for diffusion in a medium moving in a nonregular way. The author constructs generalized diffusion processes under two assumptions: first, that the diffusion matrix is sufficiently regular; and second, that the drift vector is a function integrable to some power, or is a generalized function of the type of the derivative of a measure.
Author : Charles L. Epstein
Publisher : Princeton University Press
ISBN 13 : 0691157154
Total Pages : 320 pages
Book Rating : 4.6/5 (911 download)
Download or read book Degenerate Diffusion Operators Arising in Population Biology written by Charles L. Epstein and published by Princeton University Press. This book was released on 2013-04-07 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the Martingale problem and therefore the existence of the associated Markov process. Charles Epstein and Rafe Mazzeo use an "integral kernel method" to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. Epstein and Mazzeo establish the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. They show that the semigroups defined by these operators have holomorphic extensions to the right half-plane. Epstein and Mazzeo also demonstrate precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.
Author : Dominique Bakry
Publisher : Springer Science & Business Media
ISBN 13 : 3319002279
Total Pages : 555 pages
Book Rating : 4.3/5 (19 download)
Download or read book Analysis and Geometry of Markov Diffusion Operators written by Dominique Bakry and published by Springer Science & Business Media. This book was released on 2013-11-18 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincaré, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.
Author : K.D. Elworthy
Publisher : Springer
ISBN 13 : 3540470220
Total Pages : 121 pages
Book Rating : 4.5/5 (44 download)
Download or read book On the Geometry of Diffusion Operators and Stochastic Flows written by K.D. Elworthy and published by Springer. This book was released on 2007-01-05 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properties of stochastic flows, and analysis on path spaces of compact manifolds with diffusion measures. This should be useful to stochastic analysts, especially those with interests in stochastic flows, infinite dimensional analysis, or geometric analysis, and also to researchers in sub-Riemannian geometry. A basic background in differential geometry is assumed, but the construction of the connections is very direct and itself gives an intuitive and concrete introduction. Knowledge of stochastic analysis is also assumed for later chapters.
Author : Andreas Eberle
Publisher : Springer
ISBN 13 : 3540480765
Total Pages : 265 pages
Book Rating : 4.5/5 (44 download)
Download or read book Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators written by Andreas Eberle and published by Springer. This book was released on 2007-01-05 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses both probabilists working on diffusion processes and analysts interested in linear parabolic partial differential equations with singular coefficients. The central question discussed is whether a given diffusion operator, i.e., a second order linear differential operator without zeroth order term, which is a priori defined on test functions over some (finite or infinite dimensional) state space only, uniquely determines a strongly continuous semigroup on a corresponding weighted Lp space. Particular emphasis is placed on phenomena causing non-uniqueness, as well as on the relation between different notions of uniqueness appearing in analytic and probabilistic contexts.
Author : John Crank
Publisher : Oxford University Press
ISBN 13 : 9780198534112
Total Pages : 428 pages
Book Rating : 4.5/5 (341 download)
Download or read book The Mathematics of Diffusion written by John Crank and published by Oxford University Press. This book was released on 1979 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
Author :
Publisher : ScholarlyEditions
ISBN 13 : 1490109544
Total Pages : 1182 pages
Book Rating : 4.4/5 (91 download)
Download or read book Issues in General and Specialized Mathematics Research: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in General and Specialized Mathematics Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about General Mathematics. The editors have built Issues in General and Specialized Mathematics Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General Mathematics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Author : Pierre Patie
Publisher : American Mathematical Society
ISBN 13 : 1470449366
Total Pages : 182 pages
Book Rating : 4.4/5 (74 download)
Download or read book Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups written by Pierre Patie and published by American Mathematical Society. This book was released on 2021-11-16 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Author : Wilhelm Stannat
Publisher : American Mathematical Soc.
ISBN 13 : 0821813846
Total Pages : 114 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Theory of Generalized Dirichlet Forms and Its Applications in Analysis and Stochastics written by Wilhelm Stannat and published by American Mathematical Soc.. This book was released on 1999 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explores the theory of generalized Dirichlet Forms along with its applications for analysis and stochastics. Examples are provided.
Author : Ross G. Pinsky
Publisher : Cambridge University Press
ISBN 13 : 0521470145
Total Pages : 492 pages
Book Rating : 4.5/5 (214 download)
Download or read book Positive Harmonic Functions and Diffusion written by Ross G. Pinsky and published by Cambridge University Press. This book was released on 1995-01-12 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. The book begins with a treatment of the construction and basic properties of diffusion processes. This theory then serves as a vehicle for studying positive harmonic funtions. Starting with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, the author then develops the theory of the generalized principal eigenvalue, and the related criticality theory for elliptic operators on arbitrary domains. Martin boundary theory is considered, and the Martin boundary is explicitly calculated for several classes of operators. The book provides an array of criteria for determining whether a diffusion process is transient or recurrent. Also introduced are the theory of bounded harmonic functions, and Brownian motion on manifolds of negative curvature. Many results that form the folklore of the subject are here given a rigorous exposition, making this book a useful reference for the specialist, and an excellent guide for the graduate student.
Author : Stephen Griffies
Publisher : Princeton University Press
ISBN 13 : 0691187126
Total Pages : 553 pages
Book Rating : 4.6/5 (911 download)
Download or read book Fundamentals of Ocean Climate Models written by Stephen Griffies and published by Princeton University Press. This book was released on 2018-06-05 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book sets forth the physical, mathematical, and numerical foundations of computer models used to understand and predict the global ocean climate system. Aimed at students and researchers of ocean and climate science who seek to understand the physical content of ocean model equations and numerical methods for their solution, it is largely general in formulation and employs modern mathematical techniques. It also highlights certain areas of cutting-edge research. Stephen Griffies presents material that spans a broad spectrum of issues critical for modern ocean climate models. Topics are organized into parts consisting of related chapters, with each part largely self-contained. Early chapters focus on the basic equations arising from classical mechanics and thermodynamics used to rationalize ocean fluid dynamics. These equations are then cast into a form appropriate for numerical models of finite grid resolution. Basic discretization methods are described for commonly used classes of ocean climate models. The book proceeds to focus on the parameterization of phenomena occurring at scales unresolved by the ocean model, which represents a large part of modern oceanographic research. The final part provides a tutorial on the tensor methods that are used throughout the book, in a general and elegant fashion, to formulate the equations.
Author : Hershel M. Farkas
Publisher : Springer Science & Business Media
ISBN 13 : 1461440750
Total Pages : 563 pages
Book Rating : 4.4/5 (614 download)
Download or read book From Fourier Analysis and Number Theory to Radon Transforms and Geometry written by Hershel M. Farkas and published by Springer Science & Business Media. This book was released on 2012-09-18 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: A memorial conference for Leon Ehrenpreis was held at Temple University, November 15-16, 2010. In the spirit of Ehrenpreis’s contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide breadth of subjects that Ehrenpreis traversed in his career, including partial differential equations, combinatorics, number theory, complex analysis and a bit of applied mathematics. With the exception of one survey article, the papers in this volume are all new results in the various fields in which Ehrenpreis worked . There are papers in pure analysis, papers in number theory, papers in what may be called applied mathematics such as population biology and parallel refractors and papers in partial differential equations. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore.A biographical sketch of Leon Ehrenpreis by his daughter, a professional journalist, enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician.
Author : Sergio Albeverio
Publisher : Springer
ISBN 13 : 3540449221
Total Pages : 294 pages
Book Rating : 4.5/5 (44 download)
Download or read book Lectures on Probability Theory and Statistics written by Sergio Albeverio and published by Springer. This book was released on 2003-07-03 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: In World Mathematical Year 2000 the traditional St. Flour Summer School was hosted jointly with the European Mathematical Society. Sergio Albeverio reviews the theory of Dirichlet forms, and gives applications including partial differential equations, stochastic dynamics of quantum systems, quantum fields and the geometry of loop spaces. The second text, by Walter Schachermayer, is an introduction to the basic concepts of mathematical finance, including the Bachelier and Black-Scholes models. The fundamental theorem of asset pricing is discussed in detail. Finally Michel Talagrand, gives an overview of the mean field models for spin glasses. This text is a major contribution towards the proof of certain results from physics, and includes a discussion of the Sherrington-Kirkpatrick and the p-spin interaction models.
Author : M. A. Goldberg
Publisher : Springer Science & Business Media
ISBN 13 : 1475714661
Total Pages : 351 pages
Book Rating : 4.4/5 (757 download)
Download or read book Solution Methods for Integral Equations written by M. A. Goldberg and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Feliz Manuel Minhós
Publisher : MDPI
ISBN 13 : 3036507108
Total Pages : 158 pages
Book Rating : 4.0/5 (365 download)
Download or read book Nonlinear Differential Equations and Dynamical Systems written by Feliz Manuel Minhós and published by MDPI. This book was released on 2021-04-15 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.
Author : Tamiki Komatsuzaki
Publisher : John Wiley & Sons
ISBN 13 : 111813138X
Total Pages : 403 pages
Book Rating : 4.1/5 (181 download)
Download or read book Single-Molecule Biophysics written by Tamiki Komatsuzaki and published by John Wiley & Sons. This book was released on 2011-11-16 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover the experimental and theoretical developments in optical single-molecule spectroscopy that are changing the ways we think about molecules and atoms The Advances in Chemical Physics series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. This latest volume explores the advent of optical single-molecule spectroscopy, and how atomic force microscopy has empowered novel experiments on individual biomolecules, opening up new frontiers in molecular and cell biology and leading to new theoretical approaches and insights. Organized into two parts—one experimental, the other theoretical—this volume explores advances across the field of single-molecule biophysics, presenting new perspectives on the theoretical properties of atoms and molecules. Single-molecule experiments have provided fresh perspectives on questions such as how proteins fold to specific conformations from highly heterogeneous structures, how signal transductions take place on the molecular level, and how proteins behave in membranes and living cells.This volume is designed to further contribute to the rapid development of single-molecule biophysics research. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.
