Hybrid colored noise process with space-dependent switching rates.
Hybrid colored noise process with space-dependent switching rates.
复制标题
具有空间相关开关速率的混合有色噪声处理。
DOI：
10.1103/physreve.96.012129
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
S. Lawley
中科院分区：
文献类型：
--
作者：
P. Bressloff;S. Lawley
连续随机过程理论中的一个基本问题是对乘法白噪声的解释，这通常被称为Itô-Stratonovich困境。从物理角度来看，这反映了需要引入额外的约束以指定噪声的性质，而从数学角度来看，它反映了随机微分方程（SDEs）公式中的模糊性。最近，我们已经确定了一种基于时间障碍形式获得Itô SDE的机制。受分子生物学中切换过程的启发，我们考虑了一个布朗粒子，它在具有不同扩散率的两种不同构象状态之间随机切换。在每个状态下，粒子都经历正常扩散（加性噪声），因此对噪声的解释没有歧义。然而，如果开关速率取决于位置，那么在快速开关极限下，可以得到具有Itô形式的空间相关扩散率的布朗运动。在本文中，我们将我们的理论扩展到包括彩色加性噪声。我们证明了同时取白噪声极限（κ→0）和快速开关极限（ε→0）得到的有效乘法噪声过程的性质取决于取这两个极限的顺序。如果先取白噪声极限，则得到Itô；如果先取快速开关极限，则得到Stratonovich。此外，两种情况下有效扩散系数的形式不同。后一种结果甚至适用于与空间无关的跃迁速率，即得到具有不同扩散系数的加性噪声过程。最后，我们证明了在ε/κ^{2}固定的情况下，在同时极限ε，κ→0下得到另一种形式的乘性噪声。
A fundamental issue in the theory of continuous stochastic process is the interpretation of multiplicative white noise, which is often referred to as the Itô-Stratonovich dilemma. From a physical perspective, this reflects the need to introduce additional constraints in order to specify the nature of the noise, whereas from a mathematical perspective it reflects an ambiguity in the formulation of stochastic differential equations (SDEs). Recently, we have identified a mechanism for obtaining an Itô SDE based on a form of temporal disorder. Motivated by switching processes in molecular biology, we considered a Brownian particle that randomly switches between two distinct conformational states with different diffusivities. In each state, the particle undergoes normal diffusion (additive noise) so there is no ambiguity in the interpretation of the noise. However, if the switching rates depend on position, then in the fast switching limit one obtains Brownian motion with a space-dependent diffusivity of the Itô form. In this paper, we extend our theory to include colored additive noise. We show that the nature of the effective multiplicative noise process obtained by taking both the white-noise limit (κ→0) and fast switching limit (ε→0) depends on the order the two limits are taken. If the white-noise limit is taken first, then we obtain Itô, and if the fast switching limit is taken first, then we obtain Stratonovich. Moreover, the form of the effective diffusion coefficient differs in the two cases. The latter result holds even in the case of space-independent transition rates, where one obtains additive noise processes with different diffusion coefficients. Finally, we show that yet another form of multiplicative noise is obtained in the simultaneous limit ε,κ→0 with ε/κ^{2} fixed.