Geometric and symmetry properties of a nondegenerate diffusion process

• 成果类型: Article
• 署名作者: deLara, MC
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176987794
• 发表日期: 1995
• 页码: 1557-1604
• 关键词: markov-processes

摘要

A diffusion process with smooth and nondegenerate elliptic infinitesimal generator on a manifold M induces a Riemannian metric g on M. This paper discusses in detail different symmetry properties of such a diffusion by geometric methods. Partial differential equations associated with the generator are studied likewise. With an eye to modelling and applications to filtering, relationships between symmetries of deterministic systems and symmetries of diffusion processes are delineated. The incidence of a stochastic framework on the properties of an original deterministic system are then illustrated in different examples. The construction of a diffusion process with given symmetries is also addressed and resulting geometric problems are raised.