Estimation of the Density of Hypoelliptic Diffusion Processes with Application to an Extended Itô's Formula

Xavier Bardina () and Maria Jolis ()
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Xavier Bardina: Universitat Autònoma de Barcelona
Maria Jolis: Universitat Autònoma de Barcelona

Journal of Theoretical Probability, 2002, vol. 15, issue 1, 223-247

Abstract: Abstract We prove a uniform bound for the density, p t (x), of the solution at time t∈(0, 1] of a 1-dimensional stochastic differential equation, under hypoellipticity conditions. A similar bound is obtained for an expression involving the distributional derivative (with respect to x) of p t (x). These results are applied to extend the Itô formula to the composition of a function (satisfying slight regularity conditions) with a hypoelliptic diffusion process in the spirit of the work of Föllmer et al. (5)

Keywords: estimation of densities; Hypoelliptic diffusion processes; Itô's formula; Malliavin calculus (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1013899603656

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