具有人口统计噪声的单位区间映射中逃逸事件的抑制
Suppressing escape events in maps of the unit interval with demographic noise
摘要：
研究了状态空间有界的离散随机过程的性质，其确定性极限由单位区间映射给出。我们发现，在介观描述的系统，连续迭代过程之间的大跳跃可能导致概率泄漏的单位间隔，尽管事实上，噪声是乘法和消失的边界。通过在介观展开中包含高阶项，我们能够捕获边界附近噪声分布的非高斯性质，但这并不排除轨迹离开区间的可能性。我们提出了一些治疗这些逃逸事件的处方，我们比较的结果与亚稳态行为的微观模型，逃逸事件是不可能的。我们发现，而不是截断噪声分布，审查这个分布，以防止逃逸事件导致的结果是更符合微观模型。在噪声分布中增加更高的矩不会增加最终结果的准确性，并且可以用更简单的高斯噪声来代替。
英文摘要：
We explore the properties of discrete-time stochastic processes with a bounded state space, whose deterministic limit is given by a map of the unit interval. We find that, in the mesoscopic description of the system, the large jumps between successive iterates of the process can result in probability leaking out of the unit interval, despite the fact that the noise is multiplicative and vanishes at the boundaries. By including higher-order terms in the mesoscopic expansion, we are able to capture the non-Gaussian nature of the noise distribution near the boundaries, but this does not preclude the possibility of a trajectory leaving the interval. We propose a number of prescriptions for treating these escape events, and we compare the results with those obtained for the metastable behavior of the microscopic model, where escape events are not possible. We find that, rather than truncating the noise distribution, censoring this distribution to prevent escape events leads to results which are more consistent with the microscopic model. The addition of higher moments to the noise distribution does not increase the accuracy of the final results, and it can be replaced by the simpler Gaussian noise.
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