Analytical Methods For Markov Semigroups

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Analytical Methods for Markov Semigroups

Luca Lorenzi,Marcello Bertoldi
Analytical Methods for Markov Semigroups Book PDF

Author : Luca Lorenzi,Marcello Bertoldi
Publisher : CRC Press
Page : 559 pages
File Size : 47,9 Mb
Release : 2006-07-28
Category : Mathematics
ISBN : 9781420011586

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Analytical Methods for Markov Semigroups by Luca Lorenzi,Marcello Bertoldi Pdf

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.

Analytical Methods for Kolmogorov Equations

Luca Lorenzi
Analytical Methods for Kolmogorov Equations Book PDF

Author : Luca Lorenzi
Publisher : CRC Press
Page : 572 pages
File Size : 52,9 Mb
Release : 2016-10-04
Category : Mathematics
ISBN : 9781315355627

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Analytical Methods for Kolmogorov Equations by Luca Lorenzi Pdf

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.

Markov Processes, Semigroups, and Generators

Vassili N. Kolokoltsov
Markov Processes Semigroups and Generators Book PDF

Author : Vassili N. Kolokoltsov
Publisher : Walter de Gruyter
Page : 449 pages
File Size : 48,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9783110250107

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Markov Processes, Semigroups, and Generators by Vassili N. Kolokoltsov Pdf

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

Analysis and Geometry of Markov Diffusion Operators

Dominique Bakry,Ivan Gentil,Michel Ledoux
Analysis and Geometry of Markov Diffusion Operators Book PDF

Author : Dominique Bakry,Ivan Gentil,Michel Ledoux
Publisher : Springer Science & Business Media
Page : 555 pages
File Size : 41,8 Mb
Release : 2013-11-18
Category : Mathematics
ISBN : 9783319002279

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Analysis and Geometry of Markov Diffusion Operators by Dominique Bakry,Ivan Gentil,Michel Ledoux Pdf

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.

Functional Analytic Methods for Evolution Equations

Giuseppe Da Prato,Peer Christian Kunstmann,Irena Lasiecka,Alessandra Lunardi,Roland Schnaubelt,Lutz Weis
Functional Analytic Methods for Evolution Equations Book PDF

Author : Giuseppe Da Prato,Peer Christian Kunstmann,Irena Lasiecka,Alessandra Lunardi,Roland Schnaubelt,Lutz Weis
Publisher : Springer Science & Business Media
Page : 486 pages
File Size : 42,9 Mb
Release : 2004-09-22
Category : Mathematics
ISBN : 3540230300

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Functional Analytic Methods for Evolution Equations by Giuseppe Da Prato,Peer Christian Kunstmann,Irena Lasiecka,Alessandra Lunardi,Roland Schnaubelt,Lutz Weis Pdf

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.

Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups

Eduard Yu. Emel'yanov
Non spectral Asymptotic Analysis of One Parameter Operator Semigroups Book PDF

Author : Eduard Yu. Emel'yanov
Publisher : Springer Science & Business Media
Page : 181 pages
File Size : 51,7 Mb
Release : 2007-02-17
Category : Mathematics
ISBN : 9783764381141

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Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups by Eduard Yu. Emel'yanov Pdf

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.

Markov Processes, Semigroups and Generators

Vassili N. Kolokoltsov
Markov Processes Semigroups and Generators Book PDF

Author : Vassili N. Kolokoltsov
Publisher : Walter de Gruyter
Page : 449 pages
File Size : 43,5 Mb
Release : 2011-03-29
Category : Mathematics
ISBN : 9783110250114

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Markov Processes, Semigroups and Generators by Vassili N. Kolokoltsov Pdf

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

Boundary Value Problems and Markov Processes

Kazuaki Taira
Boundary Value Problems and Markov Processes Book PDF

Author : Kazuaki Taira
Publisher : Springer
Page : 139 pages
File Size : 48,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540466352

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Boundary Value Problems and Markov Processes by Kazuaki Taira Pdf

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.

Semigroups of Operators -Theory and Applications

Jacek Banasiak,Adam Bobrowski,Mirosław Lachowicz
Semigroups of Operators Theory and Applications Book PDF

Author : Jacek Banasiak,Adam Bobrowski,Mirosław Lachowicz
Publisher : Springer
Page : 338 pages
File Size : 40,6 Mb
Release : 2014-11-20
Category : Mathematics
ISBN : 9783319121451

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Semigroups of Operators -Theory and Applications by Jacek Banasiak,Adam Bobrowski,Mirosław Lachowicz Pdf

Many results, both from semi group theory itself and from the applied sciences, are phrased in discipline-specific languages and hence are hardly known to a broader community. This volume contains a selection of lectures presented at a conference that was organised as a forum for all mathematicians using semi group theory to learn what is happening outside their own field of research. The collection will help to establish a number of new links between various sub-disciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The theory of semigroups of operators is a well-developed branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while the fundamental generation theorem of Hille and Yosida dates back to the forties. The theory was, from the very beginning, designed as a universal language for partial differential equations and stochastic processes, but at the same time it started to live as an independent branch of operator theory. Nowadays, it still has the same distinctive flavour: it develops rapidly by posing new ‘internal’ questions and in answering them, discovering new methods that can be used in applications. On the other hand, it is influenced by questions from PDEs and stochastic processes as well as from applied sciences such as mathematical biology and optimal control, and thus it continually gathers a new momentum. Researchers and postgraduate students working in operator theory, partial differential equations, probability and stochastic processes, analytical methods in biology and other natural sciences, optimization and optimal control will find this volume useful.

Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients

Haesung Lee,Wilhelm Stannat,Gerald Trutnau
Analytic Theory of It Stochastic Differential Equations with Non smooth Coefficients Book PDF

Author : Haesung Lee,Wilhelm Stannat,Gerald Trutnau
Publisher : Springer Nature
Page : 139 pages
File Size : 55,9 Mb
Release : 2022-08-27
Category : Mathematics
ISBN : 9789811938313

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Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients by Haesung Lee,Wilhelm Stannat,Gerald Trutnau Pdf

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.

Schrödinger Operators, Markov Semigroups, Wavelet Analysis, Operator Algebras

Michael Demuth
Schr dinger Operators Markov Semigroups Wavelet Analysis Operator Algebras Book PDF

Author : Michael Demuth
Publisher : De Gruyter Akademie Forschung
Page : 414 pages
File Size : 42,9 Mb
Release : 1996
Category : Mathematics
ISBN : UOM:39015041046973

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Schrödinger Operators, Markov Semigroups, Wavelet Analysis, Operator Algebras by Michael Demuth Pdf

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.

Boundary Value Problems and Markov Processes

Kazuaki Taira
Boundary Value Problems and Markov Processes Book PDF

Author : Kazuaki Taira
Publisher : Springer Nature
Page : 502 pages
File Size : 50,8 Mb
Release : 2020-07-01
Category : Mathematics
ISBN : 9783030487881

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Boundary Value Problems and Markov Processes by Kazuaki Taira Pdf

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.

Semigroups, Boundary Value Problems and Markov Processes

Kazuaki Taira
Semigroups Boundary Value Problems and Markov Processes Book PDF

Author : Kazuaki Taira
Publisher : Springer
Page : 724 pages
File Size : 44,7 Mb
Release : 2014-08-07
Category : Mathematics
ISBN : 9783662436967

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Semigroups, Boundary Value Problems and Markov Processes by Kazuaki Taira Pdf

A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and elliptic boundary value problems. The author studies a general class of elliptic boundary value problems for second-order, Waldenfels integro-differential operators in partial differential equations and proves that this class of elliptic boundary value problems provides a general class of Feller semigroups in functional analysis. As an application, the author constructs a general class of Markov processes in probability in which a Markovian particle moves both by jumps and continuously in the state space until it 'dies' at the time when it reaches the set where the particle is definitely absorbed. Augmenting the 1st edition published in 2004, this edition includes four new chapters and eight re-worked and expanded chapters. It is amply illustrated and all chapters are rounded off with Notes and Comments where bibliographical references are primarily discussed. Thanks to the kind feedback from many readers, some errors in the first edition have been corrected. In order to keep the book up-to-date, new references have been added to the bibliography. Researchers and graduate students interested in PDEs, functional analysis and probability will find this volume useful.

Functional Analysis and the Feynman Operator Calculus

Tepper Gill,Woodford Zachary
Functional Analysis and the Feynman Operator Calculus Book PDF

Author : Tepper Gill,Woodford Zachary
Publisher : Springer
Page : 354 pages
File Size : 54,5 Mb
Release : 2016-03-30
Category : Mathematics
ISBN : 9783319275956

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Functional Analysis and the Feynman Operator Calculus by Tepper Gill,Woodford Zachary Pdf

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.

Real and Complex Analysis

Christopher Apelian,Steve Surace
Real and Complex Analysis Book PDF

Author : Christopher Apelian,Steve Surace
Publisher : CRC Press
Page : 569 pages
File Size : 52,5 Mb
Release : 2009-12-08
Category : Mathematics
ISBN : 9781584888079

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Real and Complex Analysis by Christopher Apelian,Steve Surace Pdf

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.