The exit problem for diffusions with time-periodic drift and stochastic resonance
The exit problem for diffusions with time-periodic drift and stochastic resonance
复制标题
具有时间周期漂移和随机共振的扩散的退出问题
DOI：
10.1214/105051604000000530
复制
发表时间：
2005
影响因子：
1.8
通讯作者：
P. Imkeller
中科院分区：
文献类型：
--
作者：
S. Herrmann;P. Imkeller
在周期性变化的双阱势中，势扩散的随机共振物理概念如谱功率放大已被证明是有缺陷的。他们是不强大的通道，其有效的动态：连续时间有限状态马尔可夫链描述的粗糙特征之间的过渡域的吸引力的亚稳点。在一维扩散运动的周期性变化的双势阱的框架内，我们设计了一个新的概念的随机共振，它细化Freidlin的准周期运动的概念。它是基于精确的指数率之间的转移概率域的吸引力是强大的减少马尔可夫链。周期性调谐的质量通过取决于时间尺度参数的固定时间窗口期间的转变的概率来测量。在该参数中使其最大化产生随机共振点。
Physical notions of stochastic resonance for potential diffusions in periodically changing double-well potentials such as the spectral power amplification have proved to be defective. They are not robust for the passage to their effective dynamics: continuous-time finite-state Markov chains describing the rough features of transitions between different domains of attraction of metastable points. In the framework of one-dimensional diffusions moving in periodically changing double-well potentials we design a new notion of stochastic resonance which refines Freidlin's concept of quasi-periodic motion. It is based on exact exponential rates for the transition probabilities between the domains of attraction which are robust with respect to the reduced Markov chains. The quality of periodic tuning is measured by the probability for transition during fixed time windows depending on a time scale parameter. Maximizing it in this parameter produces the stochastic resonance points.