Logarithmic Estimates for the Density of Hypoelliptic Two-Parameter Diffusions

✍ Scribed by A. Kohatsu-Higa; D. Márquez-Carreras; M. Sanz-Solé

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 221 KB
• Volume: 190
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2001.3865

✦ Synopsis

We consider a hypoelliptic two-parameter diffusion. We first prove a sharp upper bound in small time (s, t) ¥ [0, 1] 2 for the L p -moments of the inverse of the Malliavin matrix of the diffusion process. Second, we establish the behaviour of 2e 2 log p s, t (x, y), as e a 0, where x is the initial condition of the diffusion, e=`st, and p s, t (x, y) is the density of the hypoelliptic two-parameter diffusion.