National Institute of Physics and Nuclear Engineering, Bucharest, Romania.
Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA.
Phys Rev E. 2017 Jun;95(6-1):062406. doi: 10.1103/PhysRevE.95.062406. Epub 2017 Jun 9.
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.
随机指数增长在多种情境下都有观察到，包括分子自催化、核裂变、种群增长、宇宙膨胀、病毒社交媒体帖子和金融市场。然而，关于这些随机动力学现象学建模的文献主要集中在一个模型上，即几何布朗运动（GBM），它可以描述为具有线性漂移和线性乘法噪声的朗之万方程的解。利用最近关于单个细菌细胞大小随机指数增长的实验结果，我们提出需要更一般的随机指数增长现象学模型类，这些模型与观察到的长时间内均值缩放分布近似稳定的结果一致。我们表明，这种行为与 GBM 不一致，而是与具有正分数幂的幂律乘法噪声一致。因此，我们考虑这种随机指数增长的一般现象学模型类，提供解析解，并确定确定均值缩放分布形状的模型参数的重要无维组合。我们还提供了一种从实验观测到的随机增长轨迹中稳健推断模型参数的方法。
