Tomasz Komorowski
Fluctuations in markov processes : time symmetry and martingale approximation - Heidelberg: Springer-Verlag, [c2012] - 491 p - Grundlehren der mathematischen Wissenschaften Vol. 345 .
Part I- General Theory
Ch 1. A Warming-Up Example
Ch 2. Central Limit Theorems
Ch 3. Random Walks in Random Environment
Ch 4. Bounds and Variational Principles for the Asymptotic Variance
Part II- Simple Exclusion Processes
Ch 5. The Simple Exclusion Process
Ch 6. Self-diffusion
Ch 7. Equilibrium Fluctuations of the Density Field
Ch 8. Regularity of the Asymptotic Variance
Part III- Diffusions in Random Environments
Ch 9. Diffusions in Random Environments
Ch 10. Variational Principles for the Limiting Variance
Ch 11. Diffusions with Divergence Free Drifts
Ch 12. Diffusions with Gaussian Drifts
Ch 13. Ornstein–Uhlenbeck Process with a Random Potential
Ch 14. Analytic Methods in Homogenization Theory
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). --- summary provided by publisher
9783642298790
Mathematics
QA 274.7
Fluctuations in markov processes : time symmetry and martingale approximation - Heidelberg: Springer-Verlag, [c2012] - 491 p - Grundlehren der mathematischen Wissenschaften Vol. 345 .
Part I- General Theory
Ch 1. A Warming-Up Example
Ch 2. Central Limit Theorems
Ch 3. Random Walks in Random Environment
Ch 4. Bounds and Variational Principles for the Asymptotic Variance
Part II- Simple Exclusion Processes
Ch 5. The Simple Exclusion Process
Ch 6. Self-diffusion
Ch 7. Equilibrium Fluctuations of the Density Field
Ch 8. Regularity of the Asymptotic Variance
Part III- Diffusions in Random Environments
Ch 9. Diffusions in Random Environments
Ch 10. Variational Principles for the Limiting Variance
Ch 11. Diffusions with Divergence Free Drifts
Ch 12. Diffusions with Gaussian Drifts
Ch 13. Ornstein–Uhlenbeck Process with a Random Potential
Ch 14. Analytic Methods in Homogenization Theory
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). --- summary provided by publisher
9783642298790
Mathematics
QA 274.7