01329nas0 22003493i 450 PUV002315720231121125607.00373-1545P 00073878P 20120510b19561992||||0itac50 barumroa|u||||||||z01i xxxe z01nCercetari de lingvistica1(1956)-2(1992)BucurestiAcademiei Republicii Socialiste Romania1956-199224 cmSemestraleLingua rumenaPeriodiciFIRRMLC361742I459.5Lingua rumena. Pubblicazioni in serie.21Academiă Republicii populare romîne : Institutul de lingvisticaSBLV117836595394312Institutul de Linguistica <Bucarest>SBLV115358Academiă Republicii populare romîne : Institutul de lingvisticaITIT-0120120510IT-FR0017 Biblioteca umanistica Giorgio ApreaFR0017 PUV0023157Biblioteca umanistica Giorgio Aprea1957 52DFAG R 10 52SBA0000136635 VPB RS A.2 (1957). Donazione Francesco AgostiniC 2012051020120510 52Cercetari de lingvistica3612927UNICAS04954oam 2200517 450 991079086800332120190911112729.0981-4452-65-3(OCoLC)860388715(MiFhGG)GVRL8RGK(EXLCZ)99255000000116007520140501h20142014 uy 0engurun|---uuuuatxtccrAnalysis for diffusion processes on Riemannian manifolds /Feng-Yu Wang, Beijing Normal University, China & Swansea University, UKNew Jersey :World Scientific,[2014]�20141 online resource (xii, 379 pages) illustrationsAdvanced Series on Statistical Science & Applied Probability ;Volume 18Description based upon print version of record.981-4452-64-5 1-306-12029-2 Includes bibliographical references and index.Preface; Contents; 1. Preliminaries; 1.1 Riemannian manifold; 1.1.1 Differentiable manifold; 1.1.2 Riemannian manifold; 1.1.3 Some formulae and comparison results; 1.2 Riemannian manifold with boundary; 1.3 Coupling and applications; 1.3.1 Transport problem and Wasserstein distance; 1.3.2 Optimal coupling and optimal map; 1.3.3 Coupling for stochastic processes; 1.3.4 Coupling by change of measure; 1.4 Harnack inequalities and applications; 1.4.1 Harnack inequality; 1.4.2 Shift Harnack inequality; 1.5 Harnack inequality and derivative estimate1.5.1 Harnack inequality and entropy-gradient estimate1.5.2 Harnack inequality and L2-gradient estimate; 1.5.3 Harnack inequalities and gradient-gradient estimates; 1.6 Functional inequalities and applications; 1.6.1 Poincar e type inequality and essential spectrum; 1.6.2 Exponential decay in the tail norm; 1.6.3 The F-Sobolev inequality; 1.6.4 Weak Poincare inequality; 1.6.5 Equivalence of irreducibility and weak Poincare inequality; 2. Diffusion Processes on Riemannian Manifolds without Boundary; 2.1 Brownian motion with drift; 2.2 Formulae for Pt and RicZ2.3 Equivalent semigroup inequalities for curvature lower bound2.4 Applications of equivalent semigroup inequalities; 2.5 Transportation-cost inequality; 2.5.1 From super Poincare to weighted log-Sobolev inequalities; 2.5.2 From log-Sobolev to transportation-cost inequalities; 2.5.3 From super Poincare to transportation-cost inequalities; 2.5.4 Super Poincare inequality by perturbations; 2.6 Log-Sobolev inequality: Different roles of Ric and Hess; 2.6.1 Exponential estimate and concentration of; 2.6.2 Harnack inequality and the log-Sobolev inequality2.6.3 Hypercontractivity and ultracontractivity2.7 Curvature-dimension condition and applications; 2.7.1 Gradient and Harnack inequalities; 2.7.2 HWI inequalities; 2.8 Intrinsic ultracontractivity on non-compact manifolds; 2.8.1 The intrinsic super Poincare inequality; 2.8.2 Curvature conditions for intrinsic ultracontractivity; 2.8.3 Some examples; 3. Reflecting Diffusion Processes on Manifolds with Boundary; 3.1 Kolmogorov equations and the Neumann problem; 3.2 Formulae for Pt, RicZ and I; 3.2.1 Formula for Pt; 3.2.2 Formulae for RicZ and I; 3.2.3 Gradient estimates3.3 Equivalent semigroup inequalities for curvature conditionand lower bound of I3.3.1 Equivalent statements for lower bounds of RicZ and I; 3.3.2 Equivalent inequalities for curvature-dimension condition and lower bound of I; 3.4 Harnack inequalities for SDEs on Rd and extension to nonconvex manifolds; 3.4.1 Construction of the coupling; 3.4.2 Harnack inequality on Rd; 3.4.3 Extension to manifolds with convex boundary; 3.4.4 Neumann semigroup on non-convex manifolds; 3.5 Functional inequalities; 3.5.1 Estimates for inequality constants on compact manifolds3.5.2 A counterexample for Bakry-Emery criterionStochastic 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.Advanced series on statistical science & applied probability ;v. 18.Riemannian manifoldsDiffusion processesRiemannian manifolds.Diffusion processes.516.373Wang Feng-Yu480857MiFhGGMiFhGGBOOK9910790868003321Analysis for diffusion processes on Riemannian manifolds255410UNINA