Displaying similar documents to “Discounted additive functionals of Markov processes”

Explicit parametrix and local limit theorems for some degenerate diffusion processes

Valentin Konakov, Stéphane Menozzi, Stanislav Molchanov (2010)

Annales de l'I.H.P. Probabilités et statistiques

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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 McKean–Singer [ (1967) 43–69] type for the density. We therefrom derive an explicit gaussian upper bound and a partial lower bound that characterize the additional singularity induced by the degeneracy. This particular representation then allows to give a local limit theorem with the usual convergence...