2013/12/05 by Konstantinos Spiliopoulos, Spiliopoulos, Konstantinos
Computer Science · Economics, Econometrics and Finance · Mathematics · #60F10 #60F99 #60G17 #60J60 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1312.1731
openalex publication_date 2013/12/05 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We consider multiple time scales systems of stochastic differential equations\nwith small noise in random environments. We prove a quenched large deviations\nprinciple with explicit characterization of the action functional. The random\nmedium is assumed to be stationary and ergodic. In the course of the proof we\nalso prove related quenched ergodic theorems for controlled diffusion processes\nin random environments that are of independent interest. The proof relies\nentirely on probabilistic arguments, allowing to obtain detailed information on\nhow the rare event occurs. We derive a control, equivalently a change of\nmeasure, that leads to the large deviations lower bound. This information on\nthe change of measure can motivate the design of asymptotically efficient Monte\nCarlo importance sampling schemes for multiscale systems in random\nenvironments.\n