论文标题
使用有效的电势方法对随机微分方程的重新归一化
Renormalization of stochastic differential equations with multiplicative noise using effective potential methods
论文作者
论文摘要
我们提出了一种新的方法，以重新构成经受乘法噪声的随机微分方程。该方法基于在高能物理学中广泛使用的有效潜力的概念，并且已经成功地应用于受加性噪声的随机微分方程的重新归一化。我们得出了单个普通随机微分方程（任意相互作用项）的一环有效电位的通用公式（前提是噪声满足一定的归一化条件）。为了说明该方法的实用性（和局限性），我们使用有效的潜力基于简化的灰色 - 斯科特反应来重新归一化化学模型。特别是，我们使用它来计算玩具模型参数（在扰动理论中）的比例依赖性，并经历短时间相关性的高斯幂律噪声。
We present a new method to renormalize stochastic differential equations subjected to multiplicative noise. The method is based on the widely used concept of effective potential in high energy physics, and has already been successfully applied to the renormalization of stochastic differential equations subjected to additive noise. We derive a general formula for the one-loop effective potential of a single ordinary stochastic differential equation (with arbitrary interaction terms) subjected to multiplicative Gaussian noise (provided the noise satisfies a certain normalization condition). To illustrate the usefulness (and limitations) of the method, we use the effective potential to renormalize a toy chemical model based on a simplified Gray-Scott reaction. In particular, we use it to compute the scale dependence of the toy model's parameters (in perturbation theory) when subjected to a Gaussian power-law noise with short time correlations.
