Functional Inequalities Markov Semigroups and Spectral Theory
Functional Inequalities Markov Semigroups and Spectral Theory

Author: Fengyu Wang

Publisher: Elsevier

Published: 2006-04-06

Total Pages: 391

ISBN-13: 0080532071

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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.

Surveys in Stochastic Processes
Surveys in Stochastic Processes

Author: Jochen Blath

Publisher: European Mathematical Society

Published: 2011

Total Pages: 270

ISBN-13: 9783037190722

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The 33rd Bernoulli Society Conference on Stochastic Processes and Their Applications was held in Berlin from July 27 to July 31, 2009. It brought together more than 600 researchers from 49 countries to discuss recent progress in the mathematical research related to stochastic processes, with applications ranging from biology to statistical mechanics, finance and climatology. This book collects survey articles highlighting new trends and focal points in the area written by plenary speakers of the conference, all of them outstanding international experts. A particular aim of this collection is to inspire young scientists to pursue research goals in the wide range of fields represented in this volume.

Analysis For Diffusion Processes On Riemannian Manifolds
Analysis For Diffusion Processes On Riemannian Manifolds

Author: Feng-yu Wang

Publisher: World Scientific

Published: 2013-09-23

Total Pages: 392

ISBN-13: 9814452661

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Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary.

Analytical Methods for Kolmogorov Equations
Analytical Methods for Kolmogorov Equations

Author: Luca Lorenzi

Publisher: CRC Press

Published: 2016-10-04

Total Pages: 572

ISBN-13: 1315355620

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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.

Festschrift Masatoshi Fukushima: In Honor Of Masatoshi Fukushima's Sanju
Festschrift Masatoshi Fukushima: In Honor Of Masatoshi Fukushima's Sanju

Author: Zhen-qing Chen

Publisher: World Scientific

Published: 2014-11-27

Total Pages: 618

ISBN-13: 981459654X

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This book contains original research papers by leading experts in the fields of probability theory, stochastic analysis, potential theory and mathematical physics. There is also a historical account on Masatoshi Fukushima's contribution to mathematics, as well as authoritative surveys on the state of the art in the field.

Harnack Inequalities for Stochastic Partial Differential Equations
Harnack Inequalities for Stochastic Partial Differential Equations

Author: Feng-Yu Wang

Publisher: Springer Science & Business Media

Published: 2013-08-13

Total Pages: 135

ISBN-13: 1461479347

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​In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling method (called coupling by change of measures) rather than the usual maximum principle in the current literature.

Optimal Transport
Optimal Transport

Author: Yann Ollivier

Publisher: Cambridge University Press

Published: 2014-08-07

Total Pages: 317

ISBN-13: 1139993623

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The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised. Through subsequent developments, particularly in recent decades, it has become a powerful modern theory. This book contains the proceedings of the summer school 'Optimal Transportation: Theory and Applications' held at the Fourier Institute in Grenoble. The event brought together mathematicians from pure and applied mathematics, astrophysics, economics and computer science. Part I of this book is devoted to introductory lecture notes accessible to graduate students, while Part II contains research papers. Together, they represent a valuable resource on both fundamental and advanced aspects of optimal transportation, its applications, and its interactions with analysis, geometry, PDE and probability, urban planning and economics. Topics covered include Ricci flow, the Euler equations, functional inequalities, curvature-dimension conditions, and traffic congestion.

Optimal Transportation
Optimal Transportation

Author: Yann Ollivier

Publisher: Cambridge University Press

Published: 2014-08-07

Total Pages: 317

ISBN-13: 110768949X

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Lecture notes and research papers on optimal transportation, its applications, and interactions with other areas of mathematics.

Asymptotic Analysis for Functional Stochastic Differential Equations
Asymptotic Analysis for Functional Stochastic Differential Equations

Author: Jianhai Bao

Publisher: Springer

Published: 2016-11-19

Total Pages: 159

ISBN-13: 3319469797

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This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity.This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.