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MALLIAVIN CALCULUS FOR LIE GROUP-VALUED 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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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.
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 three-dimensional 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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The Lie group SU(2) endowed with its canonical subriemannian structure appears as a three-dimensional 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.
