LEADER 05372nam 2200685 450 001 9910453237703321 005 20200520144314.0 010 $a981-4452-65-3 035 $a(CKB)2550000001160075 035 $a(EBL)1561248 035 $a(OCoLC)863041172 035 $a(SSID)ssj0001341105 035 $a(PQKBManifestationID)12572872 035 $a(PQKBTitleCode)TC0001341105 035 $a(PQKBWorkID)11385414 035 $a(PQKB)10195178 035 $a(MiAaPQ)EBC1561248 035 $a(WSP)00008737 035 $a(PPN)181458632 035 $a(Au-PeEL)EBL1561248 035 $a(CaPaEBR)ebr10852280 035 $a(CaONFJC)MIL543280 035 $a(EXLCZ)992550000001160075 100 $a20140401h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAnalysis for diffusion processes on Riemannian manifolds /$fFeng-Yu Wang 210 1$aSingapore :$cWorld Scientific Publishing,$d2014. 210 4$dİ2014 215 $a1 online resource (392 p.) 225 1 $aAdvanced Series on Statistical Science & Applied Probability ;$vVolume 18 300 $aDescription based upon print version of record. 311 $a981-4452-64-5 311 $a1-306-12029-2 320 $aIncludes bibliographical references and index. 327 $aPreface; 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 estimate 327 $a1.5.1 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 RicZ 327 $a2.3 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 inequality 327 $a2.6.3 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 estimates 327 $a3.3 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 manifolds 327 $a3.5.2 A counterexample for Bakry-Emery criterion 330 $aStochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary. 410 0$aAdvanced series on statistical science & applied probability ;$vVolume 18. 606 $aRiemannian manifolds 606 $aDiffusion processes 608 $aElectronic books. 615 0$aRiemannian manifolds. 615 0$aDiffusion processes. 676 $a516.373 700 $aWang$b Feng-Yu$0480857 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910453237703321 996 $aAnalysis for diffusion processes on Riemannian manifolds$9255410 997 $aUNINA