Logarithmic Estimates for the Density of Hypoelliptic Two-Parameter Diffusions |
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| Authors: | A Kohatsu-Higa D Mrquez-Carreras M Sanz-Sol |
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| Institution: | a Departament d'Economia, Universitat Pompeu Fabra, Ramon Trias Fargas 25–27, Barcelona, 08005, Spain;b Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, Barcelona, 08007, Spain |
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| Abstract: | We consider a hypoelliptic two-parameter diffusion. We first prove a sharp upper bound in small time (s, t)0, 1]2 for the Lp-moments of the inverse of the Malliavin matrix of the diffusion process. Second, we establish the behaviour of22 log ps, t(x, y), as ↓0, where x is the initial condition of the diffusion, =
, and ps, t(x, y) is the density of the hypoelliptic two-parameter diffusion. |
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| Keywords: | Malliavin calculus two-parameter Itô equations Malliavin covariance matrix logarithmic bound for the density |
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