LARGE DEVIATIONS OF THE TRAJECTORY OF EMPIRICAL DISTRIBUTIONS OF FELLER PROCESSES ON LOCALLY COMPACT SPACES

• 成果类型: Article
• 署名作者: Kraaij, Richard C.
• 署名单位: Ruhr University Bochum
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1192
• 发表日期: 2018
• 页码: 775-828
• 关键词: particle-systems; MARKOV-PROCESSES; entropy

摘要

We study the large deviation behaviour of the trajectories of empirical distributions of independent copies of time-homogeneous Feller processes on locally compact metric spaces. Under the condition that we can find a suitable core for the generator of the Feller process, we are able to define a notion of absolutely continuous trajectories of measures in terms of some topology on this core. Also, we define a Hamiltonian in terms of the linear generator and a Lagrangian as its Legendre transform. We prove the large deviation principle and show that the rate function can be decomposed as a rate function for the initial time and an integral over the Lagrangian, finite only for absolutely continuous trajectories of measures. We apply this result for diffusion and Levy processes on R-d, for pure jump processes with bounded jump kernel on arbitrary locally compact spaces and for discrete interacting particle systems. For diffusion processes, the theorem partly extends the Dawson and Gartner theorem for noninteracting copies in the sense that it only holds for time-homogeneous processes, but on the other hand it holds for processes with degenerate diffusion matrix.