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Lower bounds for the density of the law of locally elliptic Itô processes

Vlad Bally 1
1 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
Abstract : We give lower and upper bounds for the density of the law of a locally elliptic Ito process. Locally elliptic means that the ellipticity assuption holds true only if the process lies in a tube around a deterministc given curve. This represents a generalization of the classical lower and upper bounds for the density of an uniformly elliptic diffusion process but works for diffusions which may be locally degenerated, as the log-normal type diffusion for example. In this case the lower bound is no more Gaussian but has a log normal shape. This also works for Stochastic PDE's.
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https://hal.inria.fr/inria-00071695
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Submitted on : Tuesday, May 23, 2006 - 6:33:17 PM
Last modification on : Friday, February 4, 2022 - 3:13:50 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:33:43 PM

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  • HAL Id : inria-00071695, version 1

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Vlad Bally. Lower bounds for the density of the law of locally elliptic Itô processes. [Research Report] RR-4887, INRIA. 2003. ⟨inria-00071695⟩

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