Fluctuations In Markov Processes: Time Symmetry And Martingale Approximation (grundlehren Der Mathematischen Wissenschaften)
by Tomasz Komorowski /
2012 / English / PDF
3.7 MB Download
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.
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.
