Derivative formula and gradient estimates for Gruschin type semigroups

DOI10.1007/s10959-012-0427-2zbMath1334.60167arXiv1109.6738OpenAlexW2057142551MaRDI QIDQ457092

Feng-Yu Wang

Publication date: 26 September 2014

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.6738

zbMATH Keywords

stochastic differential equationMalliavin calculusdiffusion processHarnack-type inequalitygradient estimatesderivative formulaGruschin-type semigroup

Mathematics Subject Classification ID

Related Items (9)

Derivative formulas and Poincaré inequality for Kohn-Laplacian type semigroups ⋮ Bismut formula for Lions derivative of distribution-path dependent SDEs ⋮ Bismut type derivative formulae and gradient estimate for multiplicative SDEs with fractional noises ⋮ Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift ⋮ Integration by parts formula and shift Harnack inequality for stochastic equations ⋮ Transportation inequalities for Markov kernels and their applications ⋮ Bismut formula for Lions derivative of distribution dependent SDEs and applications ⋮ Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality ⋮ Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups

Cites Work

• Degenerate Fokker-Planck equations: Bismut formula, gradient estimate and Harnack inequality
• Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries
• Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality
• Large deviations and the Malliavin calculus
• Formulae for the derivatives of degenerate diffusion semigroups
• On gradient bounds for the heat kernel on the Heisenberg group
• Formulae for the derivatives of heat semigroups
• Hypoelliptic heat kernel inequalities on the Heisenberg group
• The differentiation of hypoelliptic diffusion semigroups
• A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality
• Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg
• Stochastic flows and Bismut formulas for stochastic Hamiltonian systems
• Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups
• The Malliavin Calculus and Related Topics
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