论文标题
与比例重置的对流扩散过程
An advection-diffusion process with proportional resetting
论文作者
论文摘要
本文提出了一种扩散过程，具有一种新颖的重置机制，其中该过程的幅度在随机时间内即时转换为其值的一部分。该模型由具有加性高斯白噪声和乘法泊松射击噪声项的langevin方程来描述。该分布函数遵守Pantograph方程，这是一个同时在两个幅度评估的功能偏微分方程。从这个方程式，计算了该过程的确切统计矩和稳态分布。根据每个重置中振幅的比例，指数和高斯极端之间的分布分布在指数和高斯极端之间进行插值。这些结果对于由于随机事件而突然减少随机数量成比例地减少随机数量的应用将很有用。
This paper presents a diffusion process with a novel resetting mechanism in which the amplitude of the process is instantaneously converted to a proportion of its value at random times. This model is described by a Langevin equation with both additive Gaussian white noise and multiplicative Poisson shot noise terms. The distribution function obeys a pantograph equation, a functional partial differential equation evaluated at two amplitudes simultaneously. From this equation the exact statistical moments and steady-state distribution of the process are calculated. The distribution interpolates between exponential and Gaussian extremes depending on the proportion of the amplitude lost in each reset. These results will be useful for applications in which stochastic quantities are suddenly reduced in proportion to their values due to random events.
