03586nam 2200601 450 991048061620332120180731044909.01-4704-0533-4(CKB)3360000000465111(EBL)3114166(SSID)ssj0000888802(PQKBManifestationID)11566304(PQKBTitleCode)TC0000888802(PQKBWorkID)10866476(PQKB)11249441(MiAaPQ)EBC3114166(PPN)195418166(EXLCZ)99336000000046511120150416h20092009 uy 0engur|n|---|||||txtccrBrownian Brownian motion-I /N. Chernov, D. DolgopyatProvidence, Rhode Island :American Mathematical Society,2009.©20091 online resource (208 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 198, Number 927"Volume 198, Number 927 (fourth of 6 numbers)."0-8218-4282-X Includes bibliographical references and index.""Contents""; ""Chapter 1. Introduction""; ""1.1. The model""; ""1.2. The container""; ""1.3. Billiard approximations""; ""Chapter 2. Statement of results""; ""2.1. Heavy disk in 'equilibrium' (linear motion)""; ""2.2. Heavy disk at rest (slow acceleration)""; ""2.3. Heavy disk of small size""; ""2.4. Comparison to previous works""; ""Chapter 3. Plan of the proofs""; ""3.1. General strategy""; ""3.2. Precise definitions""; ""3.3. Key technical results""; ""Chapter 4. Standard pairs and equidistribution""; ""4.1. Unstable vectors""; ""4.2. Unstable curves""""6.2. Structure of the proofs""""6.3. Short term moment estimates for V""; ""6.4. Moment estimatesâ€?a priori bounds""; ""6.5. Tightness""; ""6.6. Second moment""; ""6.7. Martingale property""; ""6.8. Transition to continuous time""; ""6.9. Uniqueness for stochastic differential equations""; ""Chapter 7. Fast slow particle""; ""Chapter 8. Small large particle""; ""Chapter 9. Open problems""; ""9.1. Collisions of the massive disk with the wall""; ""9.2. Longer time scales""; ""9.3. Stadia and the piston problem""; ""9.4. Finitely many particles""; ""9.5. Growing number of particles""""9.6. Particles of positive size""""Appendix A. Statistical properties of dispersing billiards""; ""A.1. Decay of correlations: overview""; ""A.2. Decay of correlations: extensions""; ""A.3. Large deviations""; ""A.4. Moderate deviations""; ""A.5. Nonsingularity of diffusion matrix""; ""A.6. Asymptotics of diffusion matrix""; ""Appendix B. Growth and distortion in dispersing billiards""; ""B.1. Regularity of H-curves""; ""B.2. Invariant Section Theorem""; ""B.3. The function space R""; ""Appendix C. Distortion bounds for two particle system""; ""Bibliography""; ""Index""Memoirs of the American Mathematical Society ;Volume 198, Number 927.Diffusion processesBrownian movementsLimit theorems (Probability theory)Electronic books.Diffusion processes.Brownian movements.Limit theorems (Probability theory)519.2/33Chernov Nikolai1956-300360Dolgopyat Dmitry1972-MiAaPQMiAaPQMiAaPQBOOK9910480616203321Brownian Brownian motion-I2262698UNINA