Explicit parametrix and local limit theorems for some degenerate diffusion processes
By Valentin D. Konakov, Stéphane Menozzi, Stanislav Molchanov. 2008
57 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/6607409e778d93096d50c90aeb72f44bb44d1d9e
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In Applied Mathematics
In Finance
In Statistics and Probability
Citations in the corpus
- Parametrix techniques and martingale problems for some degenerate Kolmogorov equations (2010, methodology): “On the other hand, recently, we used this technique to give a local limit theorem for the Markov chain approximation of a Langevin process [KMM10] or two-sided bounds of some more general degenerated hypoelliptic operators [DM10].”