Derivation of Fokker-Planck equations for stochastic systems under excitation of multiplicative non-Gaussian white noise
Derivation of Fokker-Planck equations for stochastic systems under excitation of multiplicative non-Gaussian white noise
复制标题
乘性非高斯白噪声激励下随机系统福克-普朗克方程的推导
DOI：
10.1016/j.jmaa.2016.09.010
复制
发表时间：
2017
影响因子：
1.3
通讯作者：
Zheng Yayun
中科院分区：
文献类型：
--
作者：
Sun Xu;Duan Jinqiao;Li Xiaofan;Liu Hua;Wang Xiangjun;Zheng Yayun
Fokker–Planck equations describe time evolution of probability densities of stochastic dynamical systems and play an important role in quantifying propagation and evolution of uncertainty. Although Fokker–Planck equations can be written explicitly for systems excited by Gaussian white noise, they have remained unknown in general for systems excited by multiplicative non-Gaussian white noise. In this paper, we derive explicit forms of Fokker–Planck equations for one dimensional systems modeled by Marcus stochastic differential equations under multiplicative non-Gaussian white noise. As examples to illustrate the theoretical results, the derived formula is used to obtain Fokker–Planck equations for nonlinear dynamical systems under excitation of (i)α-stable white noise; (ii) combined Gaussian and Poisson white noise, respectively.
