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Analytical Methods For Markov Semigroups
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Book Synopsis Analytical Methods for Markov Semigroups by : Luca Lorenzi
Download or read book Analytical Methods for Markov Semigroups written by Luca Lorenzi and published by CRC Press. This book was released on 2006-07-28 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the first time in book form, Analytical Methods for Markov Semigroups provides a comprehensive analysis on Markov semigroups both in spaces of bounded and continuous functions as well as in Lp spaces relevant to the invariant measure of the semigroup. Exploring specific techniques and results, the book collects and updates the literature associated with Markov semigroups. Divided into four parts, the book begins with the general properties of the semigroup in spaces of continuous functions: the existence of solutions to the elliptic and to the parabolic equation, uniqueness properties and counterexamples to uniqueness, and the definition and properties of the weak generator. It also examines properties of the Markov process and the connection with the uniqueness of the solutions. In the second part, the authors consider the replacement of RN with an open and unbounded domain of RN. They also discuss homogeneous Dirichlet and Neumann boundary conditions associated with the operator A. The final chapters analyze degenerate elliptic operators A and offer solutions to the problem. Using analytical methods, this book presents past and present results of Markov semigroups, making it suitable for applications in science, engineering, and economics.
Book Synopsis Analytical Methods for Kolmogorov Equations by : Luca Lorenzi
Download or read book Analytical Methods for Kolmogorov Equations written by Luca Lorenzi and published by CRC Press. This book was released on 2016-10-04 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this book has a new title that more accurately reflects the table of contents. Over the past few years, many new results have been proven in the field of partial differential equations. This edition takes those new results into account, in particular the study of nonautonomous operators with unbounded coefficients, which has received great attention. Additionally, this edition is the first to use a unified approach to contain the new results in a singular place.
Book Synopsis Markov Processes, Semigroups, and Generators by : Vassili N. Kolokoltsov
Download or read book Markov Processes, Semigroups, and Generators written by Vassili N. Kolokoltsov and published by Walter de Gruyter. This book was released on 2011 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work offers a highly useful, well developed reference on Markov processes, the universal model for random processes and evolutions. The wide range of applications, in exact sciences as well as in other areas like social studies, require a volume that offers a refresher on fundamentals before conveying the Markov processes and examples for
Book Synopsis Functional Analytic Methods for Evolution Equations by : Giuseppe Da Prato
Download or read book Functional Analytic Methods for Evolution Equations written by Giuseppe Da Prato and published by Springer Science & Business Media. This book was released on 2004-09-22 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.
Book Synopsis Analysis and Geometry of Markov Diffusion Operators by : Dominique Bakry
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 552 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.
Book Synopsis Analytical Methods for Kolmogorov Equations by : Luca Lorenzi
Download or read book Analytical Methods for Kolmogorov Equations written by Luca Lorenzi and published by CRC Press. This book was released on 2016-10-04 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this book has a new title that more accurately reflects the table of contents. Over the past few years, many new results have been proven in the field of partial differential equations. This edition takes those new results into account, in particular the study of nonautonomous operators with unbounded coefficients, which has received great attention. Additionally, this edition is the first to use a unified approach to contain the new results in a singular place.
Book Synopsis Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients by : Haesung Lee
Download or read book Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients written by Haesung Lee and published by Springer Nature. This book was released on 2022-08-27 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides analytic tools to describe local and global behavior of solutions to Itô-stochastic differential equations with non-degenerate Sobolev diffusion coefficients and locally integrable drift. Regularity theory of partial differential equations is applied to construct such solutions and to obtain strong Feller properties, irreducibility, Krylov-type estimates, moment inequalities, various types of non-explosion criteria, and long time behavior, e.g., transience, recurrence, and convergence to stationarity. The approach is based on the realization of the transition semigroup associated with the solution of a stochastic differential equation as a strongly continuous semigroup in the Lp-space with respect to a weight that plays the role of a sub-stationary or stationary density. This way we obtain in particular a rigorous functional analytic description of the generator of the solution of a stochastic differential equation and its full domain. The existence of such a weight is shown under broad assumptions on the coefficients. A remarkable fact is that although the weight may not be unique, many important results are independent of it. Given such a weight and semigroup, one can construct and further analyze in detail a weak solution to the stochastic differential equation combining variational techniques, regularity theory for partial differential equations, potential, and generalized Dirichlet form theory. Under classical-like or various other criteria for non-explosion we obtain as one of our main applications the existence of a pathwise unique and strong solution with an infinite lifetime. These results substantially supplement the classical case of locally Lipschitz or monotone coefficients.We further treat other types of uniqueness and non-uniqueness questions, such as uniqueness and non-uniqueness of the mentioned weights and uniqueness in law, in a certain sense, of the solution.
Book Synopsis Markov Processes, Semigroups and Generators by : Vassili N. Kolokoltsov
Download or read book Markov Processes, Semigroups and Generators written by Vassili N. Kolokoltsov and published by Walter de Gruyter. This book was released on 2011-03-29 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov processes represent a universal model for a large variety of real life random evolutions. The wide flow of new ideas, tools, methods and applications constantly pours into the ever-growing stream of research on Markov processes that rapidly spreads over new fields of natural and social sciences, creating new streamlined logical paths to its turbulent boundary. Even if a given process is not Markov, it can be often inserted into a larger Markov one (Markovianization procedure) by including the key historic parameters into the state space. This monograph gives a concise, but systematic and self-contained, exposition of the essentials of Markov processes, together with recent achievements, working from the "physical picture" - a formal pre-generator, and stressing the interplay between probabilistic (stochastic differential equations) and analytic (semigroups) tools. The book will be useful to students and researchers. Part I can be used for a one-semester course on Brownian motion, Lévy and Markov processes, or on probabilistic methods for PDE. Part II mainly contains the author's research on Markov processes. From the contents: Tools from Probability and Analysis Brownian motion Markov processes and martingales SDE, ψDE and martingale problems Processes in Euclidean spaces Processes in domains with a boundary Heat kernels for stable-like processes Continuous-time random walks and fractional dynamics Complex chains and Feynman integral
Book Synopsis Boundary Value Problems and Markov Processes by : Kazuaki Taira
Download or read book Boundary Value Problems and Markov Processes written by Kazuaki Taira and published by Springer. This book was released on 2006-11-15 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focussing on the interrelations of the subjects of Markov processes, analytic semigroups and elliptic boundary value problems, this monograph provides a careful and accessible exposition of functional methods in stochastic analysis. The author studies a class of boundary value problems for second-order elliptic differential operators which includes as particular cases the Dirichlet and Neumann problems, and proves that this class of boundary value problems provides a new example of analytic semigroups both in the Lp topology and in the topology of uniform convergence. As an application, one can construct analytic semigroups corresponding to the diffusion phenomenon of a Markovian particle moving continuously in the state space until it "dies", at which time it reaches the set where the absorption phenomenon occurs. A class of initial-boundary value problems for semilinear parabolic differential equations is also considered. This monograph will appeal to both advanced students and researchers as an introduction to the three interrelated subjects in analysis, providing powerful methods for continuing research.
Book Synopsis Functional Analysis and the Feynman Operator Calculus by : Tepper Gill
Download or read book Functional Analysis and the Feynman Operator Calculus written by Tepper Gill and published by Springer. This book was released on 2016-03-30 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting. In one application, the results are used to prove the last two remaining conjectures of Freeman Dyson for quantum electrodynamics. In another application, the results are used to unify methods and weaken domain requirements for non-autonomous evolution equations. Other applications include a general theory of Lebesgue measure on Banach spaces with a Schauder basis and a new approach to the structure theory of operators on uniformly convex Banach spaces. This book is intended for advanced graduate students and researchers.
Book Synopsis Real and Complex Analysis by : Christopher Apelian
Download or read book Real and Complex Analysis written by Christopher Apelian and published by CRC Press. This book was released on 2009-12-08 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents Real & Complex Analysis Together Using a Unified Approach A two-semester course in analysis at the advanced undergraduate or first-year graduate level Unlike other undergraduate-level texts, Real and Complex Analysis develops both the real and complex theory together. It takes a unified, elegant approach to the theory that is consistent with the recommendations of the MAA’s 2004 Curriculum Guide. By presenting real and complex analysis together, the authors illustrate the connections and differences between these two branches of analysis right from the beginning. This combined development also allows for a more streamlined approach to real and complex function theory. Enhanced by more than 1,000 exercises, the text covers all the essential topics usually found in separate treatments of real analysis and complex analysis. Ancillary materials are available on the book’s website. This book offers a unique, comprehensive presentation of both real and complex analysis. Consequently, students will no longer have to use two separate textbooks—one for real function theory and one for complex function theory.
Book Synopsis Elements of Real Analysis by : M.A. Al-Gwaiz
Download or read book Elements of Real Analysis written by M.A. Al-Gwaiz and published by CRC Press. This book was released on 2006-08-21 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on one of the main pillars of mathematics, Elements of Real Analysis provides a solid foundation in analysis, stressing the importance of two elements. The first building block comprises analytical skills and structures needed for handling the basic notions of limits and continuity in a simple concrete setting while the second component involves conducting analysis in higher dimensions and more abstract spaces. Largely self-contained, the book begins with the fundamental axioms of the real number system and gradually develops the core of real analysis. The first few chapters present the essentials needed for analysis, including the concepts of sets, relations, and functions. The following chapters cover the theory of calculus on the real line, exploring limits, convergence tests, several functions such as monotonic and continuous, power series, and theorems like mean value, Taylor's, and Darboux's. The final chapters focus on more advanced theory, in particular, the Lebesgue theory of measure and integration. Requiring only basic knowledge of elementary calculus, this textbook presents the necessary material for a first course in real analysis. Developed by experts who teach such courses, it is ideal for undergraduate students in mathematics and related disciplines, such as engineering, statistics, computer science, and physics, to understand the foundations of real analysis.
Book Synopsis Schrödinger Operators, Markov Semigroups, Wavelet Analysis, Operator Algebras by : Michael Demuth
Download or read book Schrödinger Operators, Markov Semigroups, Wavelet Analysis, Operator Algebras written by Michael Demuth and published by De Gruyter Akademie Forschung. This book was released on 1996 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of partial differential equations has stimulated large areas of research in mathematical physics, harmonic analysis, and operator theory. The present volume illuminates the depth and variety of these interactions. It begins with a survey on the use of semiclassical analysis and maximum-principle techniques in statistical mechanics. There follows an article presenting the perturbation theory for generators of Markov semigroups acting on Lp. The third contribution provides a self-contained introduction to continuous wavelet analysis, including its relations to function spaces and microlocal regularity; this is particularly topical, as wavelet methods have been applied with great success in the past decade to problems in harmonic and numerical analysis as well as in diverse fields of engineering. The final section explores pseudo-differential analysis on singular configurations, with special emphasis on C-algebra techniques, Mellin operators, and analytical index formulas.
Book Synopsis Functional Inequalities Markov Semigroups and Spectral Theory by : Fengyu Wang
Download or read book Functional Inequalities Markov Semigroups and Spectral Theory written by Fengyu Wang and published by Elsevier. This book was released on 2006-04-06 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the functional inequalities are introduced to describe: (i) the spectrum of the generator: the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap; (ii) the semigroup properties: the uniform intergrability, the compactness, the convergence rate, and the existence of density; (iii) the reference measure and the intrinsic metric: the concentration, the isoperimetic inequality, and the transportation cost inequality.
Author :Eduard Yu. Emel'yanov Publisher :Springer Science & Business Media ISBN 13 :3764381140 Total Pages :181 pages Book Rating :4.7/5 (643 download)
Book Synopsis Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups by : Eduard Yu. Emel'yanov
Download or read book Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups written by Eduard Yu. Emel'yanov and published by Springer Science & Business Media. This book was released on 2007-02-17 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, non-spectral methods are presented and discussed that have been developed over the last two decades for the investigation of asymptotic behavior of operator semigroups. This concerns in particular Markov semigroups in L1-spaces, motivated by applications to probability theory and dynamical systems. Related results, historical notes, exercises, and open problems accompany each chapter.
Book Synopsis Boundary Value Problems and Markov Processes by : Kazuaki Taira
Download or read book Boundary Value Problems and Markov Processes written by Kazuaki Taira and published by Springer Nature. This book was released on 2020-07-01 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 3rd edition provides an insight into the mathematical crossroads formed by functional analysis (the macroscopic approach), partial differential equations (the mesoscopic approach) and probability (the microscopic approach) via the mathematics needed for the hard parts of Markov processes. It brings these three fields of analysis together, providing a comprehensive study of Markov processes from a broad perspective. The material is carefully and effectively explained, resulting in a surprisingly readable account of the subject. The main focus is on a powerful method for future research in elliptic boundary value problems and Markov processes via semigroups, the Boutet de Monvel calculus. A broad spectrum of readers will easily appreciate the stochastic intuition that this edition conveys. In fact, the book will provide a solid foundation for both researchers and graduate students in pure and applied mathematics interested in functional analysis, partial differential equations, Markov processes and the theory of pseudo-differential operators, a modern version of the classical potential theory.
Book Synopsis Multiscale Methods by : G A Pavliotis
Download or read book Multiscale Methods written by G A Pavliotis and published by Springer Science & Business Media. This book was released on 2008-02-19 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to multiscale methods gives you a broad overview of the methods’ many uses and applications. The book begins by setting the theoretical foundations of the methods and then moves on to develop models and prove theorems. Extensive use of examples shows how to apply multiscale methods to solving a variety of problems. Exercises then enable you to build your own skills and put them into practice. Extensions and generalizations of the results presented in the book, as well as references to the literature, are provided in the Discussion and Bibliography section at the end of each chapter.With the exception of Chapter One, all chapters are supplemented with exercises.
