Hypoelliptic non-homogeneous diffusions

• 成果类型: Article
• 署名作者: Cattiaux, P; Mesnager, L
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Nanterre
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400100194
• 发表日期: 2002
• 页码: 453-483
• 关键词: 2nd-order degenerate operators; stochastic calculus; asymptotic development; BOUNDARY

摘要

Let L-1 = 1/2 Sigma(i.j=1)(d) a(ij)(t, x)partial derivative(i)partial derivative(j) + Sigma(i=1)(d) b(i)(t, x)partial derivative(i) = 1/2Sigma(j=1)(m) X-j(2) (t, x) + X-0(t, x) be a time dependent second order operator, written in usual or Hormander form. We study the regularity of the law of the associated non-homogeneous (time dependent) diffusion process, under Hormander's like conditions. Coefficients are only Holder continuous in time. The main tool is Malliavin calculus. Our results extend and correct previous ones ([17] and related works, [15]). Related topics like filtering theory, killed or reflected processes, parabolic hypoellipticity are also discussed.