An integral inequality  for the   invariant measure  of  some finite dimensional stochastic differential equation

Prato, Giuseppe Da

doi:10.3934/dcdsb.2016085

Cited by 1 publication

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References 10 publications

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“…See [3,31,25] for its use in infinite dimensional analysis and for identifying Dirichlet spaces, and see [22] for its study in connection with Hamilton-Jacob equations. Differential formulas for Feynman-Kac semigroups were obtained in [21,20,16,15,43], for partial differential equations and for stochastic partial differential equations. Heat kernel formula for Schrödinger type operator acting on sections of vector bundles can be found in [49] and [11].…”

Section: Introductionmentioning

confidence: 99%

First order Feynman–Kac formula

Thompson

2018

Stochastic Processes and their Applications

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We study the parabolic integral kernel for the weighted Laplacian with a potential. For manifolds with a pole we deduce formulas and estimates for the derivatives of the Feynman-Kac kernels and their logarithms, these are in terms of a 'Gaussian' term and the semi-classical bridge.AMS Mathematics Subject Classification : 60J60, 60H30, 58J65, 58J70 key words: manifold with a pole, semi-classical bridge, Feynman-Kac formula, Gaussian bounds for fundamental solutions of parabolic equations, logarithmic heat kernels t etc. will be used. We use L ∞ , C k , BC k , C ∞ K , and C 1,α to denote respectively the set of essentially bounded measurable (real valued) functions, the set of functions (or differential forms) whose derivatives up to order k exist and are continuous, the set of bounded C k functions with bounded derivatives, the set of C k functions with

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