论文标题
通过异常缩放对大偏差的噪声纠正
Noise correction of large deviations with anomalous scaling
论文作者
论文摘要
我们提出了与Ornstein-Uhlenbeck过程的时间集成矩相关的概率分布的路径积分计算，该过程包括高斯先前取得因子，除了在低噪声限制中获得的主要路径或intsanton项外。 instanton术语最近获得了[D. Nickelsen，H。Touchette，物理。莱特牧师。 121，090602（2018）]，并表明时间融合矩的巨大偏差是异常的，因为它们的分布的对数与集成时间非线性缩放。高斯的先景因子对低噪声近似进行了校正，并导致我们定义了intsanton差异，从而有一些关于如何及时创建异常大偏差的见解。将结果与基于重要性采样的模拟进行了比较，从而根据直接的蒙特卡洛模拟扩展了我们先前的结果。我们通过解释了为什么大偏差理论的许多标准分析和数值方法在异常大偏差的情况下失败。
We present a path integral calculation of the probability distribution associated with the time-integrated moments of the Ornstein-Uhlenbeck process that includes the Gaussian prefactor in addition to the dominant path or instanton term obtained in the low-noise limit. The instanton term was obtained recently [D. Nickelsen, H. Touchette, Phys. Rev. Lett. 121, 090602 (2018)] and shows that the large deviations of the time-integrated moments are anomalous in the sense that the logarithm of their distribution scales nonlinearly with the integration time. The Gaussian prefactor gives a correction to the low-noise approximation and leads us to define an instanton variance giving some insights as to how anomalous large deviations are created in time. The results are compared with simulations based on importance sampling, extending our previous results based on direct Monte Carlo simulations. We conclude by explaining why many of the standard analytical and numerical methods of large deviation theory fail in the case of anomalous large deviations.
