Fluctuations in Markov processes : time symmetry and martingale approximation
 Author/Creator
 Komorowski, Tomasz, 1963
 Language
 English.
 Imprint
 Heidelberg [Germany] ; New York : Springer, c2012.
 Physical description
 xvii, 491 p. ; 24 cm.
 Series
 Grundlehren der mathematischen Wissenschaften ; 345.
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Contributors
 Contributor
 Landim, Claudio, 1965
 Olla, Stefano, 1959
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 475486) and index.
 Contents

 Preface. Part I: General Theory. 1.A Warmingup Example. 2.Central Limit Theorems. 3.RandomWalks in Random Environment. 4.Bounds and Variational Principles for the Asymptotic Variance. Part II: Simple Exclusion Processes. 5.The Simple Exclusion Process. 6.Self Diffusion. 7.Equilibrium Fluctuations of the Density Field. 8.Regularity of the Asymptotic Variance. Part III: Diffusions in Random Environments. 10.Variational Principles for the Limiting Variance. 11.Diffusions with Divergence Free Drifts. 12.Diffusions with Gaussian Drifts. 13.OrnsteinUhlenbeck Process with a Random Potential. 14.Analytic Methods in Homogenization Theory. References. Notation. Subject Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional models that appear in statistical mechanics and engineering (interacting particle systems, homogenization in random environments, and diffusion in turbulent flows, to mention just a few applications). The first part contains a detailed exposition of the method, and can be used as a text for graduate courses. The second concerns application to exclusion processes, in which the duality methods are fully exploited. The third part is about the homogenization of diffusions in random fields, including passive tracers in turbulent flows (including the superdiffusive behavior). There are no other books in the mathematical literature that deal with this kind of approach to the problem of the central limit theorem. Hence, this volume meets the demand for a monograph on this powerful approach, now widely used in many areas of probability and mathematical physics. The book also covers the connections with and application to hydrodynamic limits and homogenization theory, so besides probability researchers it will also be of interest also to mathematical physicists and analysts.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 Tomasz Komorowski, Claudio Landim, Stefano Olla.
 Title Variation
 Time symmetry and martingale approximation
 Series
 Grundlehren der mathematischen Wissenschaften : a series of comprehensive studies in mathematics, 00727830 ; 345
 ISBN
 3642298796 (acidfree paper)
 9783642298790 (acidfree paper)
 364229880X (eBook)
 9783642298806 (eBook)