Results 1  10
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16
Curvaturedimension inequalities and Ricci lower bounds for subRiemannian manifolds with transverse symmetries
, 2012
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Hypoelliptic heat kernel inequalities on the Heisenberg group,
 J. Func. Analysis
, 2005
"... Abstract We study the existence of "L p type"gradient estimates for the heat kernel of the natural hypoelliptic "Laplacian"on the real threedimensional Heisenberg Lie group. Using Malliavin calculus methods, we verify that these estimates hold in the case p > 1. The gradien ..."
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Cited by 26 (2 self)
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Abstract We study the existence of "L p type"gradient estimates for the heat kernel of the natural hypoelliptic "Laplacian"on the real threedimensional Heisenberg Lie group. Using Malliavin calculus methods, we verify that these estimates hold in the case p > 1. The gradient estimate for p = 2 implies a corresponding Poincaré inequality for the heat kernel. The gradient estimate for p = 1 is still open; if proved, this estimate would imply a logarithmic Sobolev inequality for the heat kernel.
LogSobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality
 J. Funct. Anal
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The subelliptic heat kernel on SU(2): Representations, Asymptotics and Gradient bounds
, 2008
"... The Lie group SU(2) endowed with its canonical subriemannian structure appears as a threedimensional model of a positively curved subelliptic space. The goal of this work is to study the subelliptic heat kernel on it and some related functional inequalities. ..."
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Cited by 19 (9 self)
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The Lie group SU(2) endowed with its canonical subriemannian structure appears as a threedimensional model of a positively curved subelliptic space. The goal of this work is to study the subelliptic heat kernel on it and some related functional inequalities.
Teichmann: OrnsteinUhlenbeck processes on Lie groups
 J. Funct. Analysis
"... Abstract. We consider OrnsteinUhlenbeck processes (OUprocesses) associated to hypoelliptic diffusion processes on finitedimensional Lie groups: let L be a hypoelliptic, leftinvariant “sum of the squares”operator on a Lie group G with associated Markov process X, then we construct OUprocesses b ..."
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Cited by 9 (1 self)
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Abstract. We consider OrnsteinUhlenbeck processes (OUprocesses) associated to hypoelliptic diffusion processes on finitedimensional Lie groups: let L be a hypoelliptic, leftinvariant “sum of the squares”operator on a Lie group G with associated Markov process X, then we construct OUprocesses by adding negative horizontal gradient drifts of functions U. In the natural case U(x) = − log p(1, x), where p(1, x) is the density of the law of X starting at identity e at time t = 1 with respect to the rightinvariant Haar measure on G, we show the Poincaré inequality by applying the DriverMelcher inequality for “sum of the squares ” operators on Lie groups. The resulting Markov process is called the natural OUprocess associated to the hypoelliptic diffusion on G. We prove the global strong existence of these OUtype processes on G under an integrability assumption on U. The Poincaré inequality for a large class of potentials U is then shown by a perturbation technique. These results are applied to obtain a hypoelliptic equivalent of standard results on cooling schedules for simulated annealing on compact homogeneous spaces M. 1.
Gradient Estimates for the Subelliptic Heat Kernel on Htype Groups
, 2009
"... We prove the following gradient inequality for the subelliptic heat kernel on nilpotent Lie groups G of Htype: ∇Ptf  ≤ KPt(∇f) where Pt is the heat semigroup corresponding to the sublaplacian on G, ∇ is the subelliptic gradient, and K is a constant. This extends a result of H.Q. Li [10] for ..."
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Cited by 6 (1 self)
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We prove the following gradient inequality for the subelliptic heat kernel on nilpotent Lie groups G of Htype: ∇Ptf  ≤ KPt(∇f) where Pt is the heat semigroup corresponding to the sublaplacian on G, ∇ is the subelliptic gradient, and K is a constant. This extends a result of H.Q. Li [10] for the Heisenberg group. The proof is based on pointwise heat kernel estimates, and follows an approach used by Bakry, Baudoin, Bonnefont, and Chafaï [3].
Ergodicity of Markov Semigroups with Hörmander Type Generators
 in Infinite Dimensions, Potential Analysis, October 2012, Volume 37, Issue 3, 199
"... Abstract: We develop an effective strategy for proving strong ergodicity of (nonsymmetric) Markov semigroups associated to Hörmander type generators when the underlying configuration space is infinite dimensional. ..."
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Cited by 4 (2 self)
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Abstract: We develop an effective strategy for proving strong ergodicity of (nonsymmetric) Markov semigroups associated to Hörmander type generators when the underlying configuration space is infinite dimensional.
Smoothness of density for the area process of fractional Brownian motion. ArXiv eprints 1010.3047
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MALLIAVIN CALCULUS FOR LIE GROUPVALUED WIENER FUNCTIONS
, 2005
"... Abstract. Let G be a Lie group equipped with a set of left invariant vector fields. These vector fields generate a function ξ on Wiener space into G via the stochastic version of Cartan’s rolling map. It is shown here that, for any smooth function f with compact support, f(ξ) is Malliavin differenti ..."
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Cited by 3 (3 self)
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Abstract. Let G be a Lie group equipped with a set of left invariant vector fields. These vector fields generate a function ξ on Wiener space into G via the stochastic version of Cartan’s rolling map. It is shown here that, for any smooth function f with compact support, f(ξ) is Malliavin differentiable to all orders and these derivatives belong to L p (µ) for all p> 1, where µ is Wiener measure.