扩散过程Gallavotti-Cohen泛函的小噪声渐近性
Small noise asymptotic of the Gallavotti-Cohen functional for diffusion processes
摘要：
对于R^n中的扩散过程，我们考虑Gallavotti-Cohen泛函，定义为漂移的非保守部分在一定时间间隔内耗散的经验功率.我们证明了在噪声消失和时间间隔发散的极限下的一个大偏差原理。相应的速率泛函满足涨落定理，表示为经典Freidlin-Wentzell泛函上的一个变分问题。
英文摘要：
We consider, for a diffusion process in R^n, the Gallavotti-Cohen functional, defined as the empirical power dissipated in a time interval by the non-conservative part of the drift. We prove a large deviation principle in the limit in which the noise vanishes and the time interval diverges. The corresponding rate functional, which satisfies the fluctuation theorem, is expressed in terms of a variational problem on the classical Freidlin-Wentzell functional.
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