Explicit parametrix and local limit theorems for some degenerate diffusion processes

Abstract : For a class of degenerate diffusion processes of rank 2, i.e. when only Poisson brackets of order one are needed to span the whole space, we obtain a parametrix representation of the density from which we derive some explicit Gaussian controls that characterize the additional singularity induced by the degeneracy. We then give a local limit theorem with the usual convergence rate for an associated Markov chain approximation. The key point is that the "weak" degeneracy allows to exploit the techniques first introduced by Konakov and Molchanov and then developed by Konakov and Mammen that rely on Gaussian approximations.
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https://hal.archives-ouvertes.fr/hal-00256588
Contributor : Stephane Menozzi <>
Submitted on : Wednesday, February 18, 2009 - 4:19:30 PM
Last modification on : Wednesday, August 21, 2019 - 10:22:04 AM
Long-term archiving on : Wednesday, September 22, 2010 - 12:04:10 PM

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  • HAL Id : hal-00256588, version 2
  • ARXIV : 0802.2229

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Valentin Konakov, Stephane Menozzi, Stanislav Molchanov. Explicit parametrix and local limit theorems for some degenerate diffusion processes. Annales de l'Institut Henri Poincaré, 2010, 46 (4), pp.908-923. ⟨https://projecteuclid.org/euclid.aihp/1288878329⟩. ⟨hal-00256588v2⟩

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