Analysis for Diffusion Processes on Riemannian Manifolds

Wang, Feng‐Yu

doi:10.1142/8737

Cited by 89 publications

(137 citation statements)

References 0 publications

Supporting

Mentioning

134

Contrasting

Order By: Relevance

“…Since then, it has been extensively studied in the literature. Feng-Yu Wang is one of the leading persons on this topic and we refer to his books [42,44] for further developments. A coupling admitting different time scales is studied also in [28,33].…”

Section: Introductionmentioning

confidence: 99%

Space-time Wasserstein controls and Bakry–Ledoux type gradient estimates

Kuwada

2014

Calc. Var.

View full text Add to dashboard Cite

The duality in Bakry-Émery's gradient estimates and Wasserstein controls for heat distributions is extended to that in refined estimates in a high generality. As a result, we find an equivalent condition to Bakry-Ledoux's refined gradient estimate involving an upper dimension bound. This new condition is described as a L 2 -Wasserstein control for heat distributions at different times. The L p -version of those estimates are studied on Riemannian manifolds via coupling method. Mathematics Subject Classification

show abstract

Section: Introductionmentioning

confidence: 99%

Space-time Wasserstein controls and Bakry–Ledoux type gradient estimates

Kuwada

2014

Calc. Var.

View full text Add to dashboard Cite

show abstract

“…First, we introduce Hsu's multiplicative functionals {Q x s,t } 0 s t<Tc (see [13]) by using Wang's method (see [17,Theorem 4.1.1]) to simplify the construction. These functionals are applied to establishing the derivative formula for the diffusion semigroup {P s,t } 0 s t<Tc , known as the Bismut-Elworthy-Li formula (see [2,8] on manifolds with constant metric).…”

Section: Assumption Amentioning

confidence: 99%

An integration by parts formula on path space over manifolds carrying geometric flow

Cheng

2015

Sci. China Math.

View full text Add to dashboard Cite

We establish an integration by parts formula on the path space with reference measure P, the law of the (reflecting) diffusion process on manifolds with possible boundary carrying geometric flow, which leads to the standard log-Sobolev inequality for the associated Dirichlet form. To this end, we first modify Hsu's multiplicative functionals to define the damp gradient operator, which links to quasi-invariant flows; and then establish the derivative formula for the associated inhomogeneous diffusion semigroup. Keywordsintegration by parts formula, geometric flow, log-Sobolev inequality, path space over manifolds with boundary, reflecting Lt-diffusion process MSC(2010) 60J60, 58J65, 53C44Citation: Cheng L J. An integration by parts formula on path space over manifolds carrying geometric flow.

show abstract

“…[1,2,3,4,10,11,14,15,16,17,22,25,26,28,29,30,32,33,34,35] and the references therein for a very noncomprehensive excerpt). In the study of n-dimensional weighted-manifolds satisfying CD(ρ, N ), the range of admissible values for N has traditionally been N ∈ [n, ∞].…”

Section: Introductionmentioning

confidence: 99%

Harmonic Measures on the Sphere via Curvature-Dimension

Milman¹

2017

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

View full text Add to dashboard Cite

Analysis for Diffusion Processes on Riemannian Manifolds

Cited by 89 publications

References 0 publications

Space-time Wasserstein controls and Bakry–Ledoux type gradient estimates

Space-time Wasserstein controls and Bakry–Ledoux type gradient estimates

An integration by parts formula on path space over manifolds carrying geometric flow

Harmonic Measures on the Sphere via Curvature-Dimension

Contact Info

Product

Resources

About