Beyond Ito versus Stratonovich
添加于 2012/9/18 15:25:34 1598次阅读 | 2次推荐 | 5个评论
Recently, a novel framework to handle stochastic processes has emerged from a series of studies in biology, showing situations beyond 'Ito versus Stratonovich'. Its internal consistency can be demonstrated via the zero mass limit of a generalized Klein-Kramers equation. Moreover, the connection to other integrations becomes evident: the obtained Fokker-Planck equation defines a new type of stochastic calculus that in general differs from the alpha-type interpretation. A unique advantage of this new approach is a natural correspondence between stochastic and deterministic dynamics, which is useful or may even be essential in practice. The core of the framework is a transformation from the usual Langevin equation to a form that contains a potential function with two additional dynamical matrices, which reveals an underlying symplectic structure. The framework has a direct physical meaning and a straightforward experimental realization. A recent experiment has offered a first empirical validation of this new stochastic integration.
Ruoshi Yuan and Ping Ao
Journal of Statistical Mechanics: Theory and Experiment
第2012卷 第07期 P07010~页
数理科学 » 数学 » 常微分方程与动力系统
energy landscapes (theory),systems biology,stochastic processes (theory),brownian motion