Path integral solutions for n-dimensional stochastic differential equations underα-stable Lévy excitation  

作　　者：Wanrong Zan Yong Xu Jürgen Kurths 

机构地区：[1]School of Mathematics,Northwest University,Xi’an,710127,China [2]Department of Applied Mathematics,Northwestern Polytechnical University,Xi’an,710129,China [3]MIIT key Laboratory of Dynamics and Control of Complex Systems,Northwestern Polytechnical University,Xi’an,710129,China [4]Potsdam Institute for Climate Impact Research,Potsdam,14412,Germany [5]Department of Physics,Humboldt University of Berlin,Berlin,12489,Germany

出　　处：《Theoretical & Applied Mechanics Letters》2023年第2期98-112,共15页力学快报（英文版）

基　　金：This work was supported by the Key International(Regional)Joint Research Program of the National Natural Science Foundation of China(No.12120101002).

摘　　要：In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and verified.Firstly,the governing equations for the solutions of n-dimensional SDEs under the excitation ofα-stable Lévy noise are obtained through the characteristic function of stochastic processes.Then,the short-time transition probability density func-tion of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski(CKS)equation and the characteristic function,and its correctness is demonstrated by proving that it satis-fies the governing equation of the solution of the SDE,which is also called the Fokker-Planck-Kolmogorov equation.Besides,illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method,and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.

关 键 词：Path integral method α-stable Lévy noise Monte carlo method Fokker-Planck-Kolmogorov equation 

分 类 号：O211.63[理学—概率论与数理统计]