We propose a simple Langevin equation as a generator for a noise process with Laplace-distributed values (pure exponential decays for both positive and negative values of the noise). We calculate explicit expressions for the correlation function, the noise intensity, and the correlation time of this noise process and formulate a scaled version of the generating Langevin equation such that correlation time and variance or correlation time and noise intensity for the desired noise process can be exactly prescribed. We then test the effect of the noise distribution on a classical escape problem: the Kramers rate of an overdamped particle out of the minimum of a cubic potential. We study the problem both for constant variance and constant intensity scalings and compare to an Ornstein–Uhlenbeck process with the same noise parameters. We demonstrate that specifically at weak fluctuations, the Laplace noise induces more frequent escapes than its Gaussian counterpart while at stronger noise the opposite effect is observed.

我们提出一个简单的Langevin方程作为噪声过程的生成器，该过程具有拉普拉斯分布的值（噪声的正值和负值都具有纯指数衰减）。我们计算该噪声过程的相关函数，噪声强度和相关时间的显式表达式，并公式化生成的Langevin方程的缩放比例，以便可以将所需噪声过程的相关时间和方差或相关时间和噪声强度设为确切地规定。然后，我们测试噪声分布对经典逃逸问题的影响：过度阻尼的粒子的Kramers速率超出立方势的最小值。我们研究了恒定方差和恒定强度缩放的问题，并与具有相同噪声参数的Ornstein-Uhlenbeck过程进行了比较。