TY - JOUR
T1 - Path integral solutions of the governing equation of SDEs excited by Lévy white noise
AU - Xu, Yong
AU - Zan, Wanrong
AU - Jia, Wantao
AU - Kurths, Jürgen
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2019/10/1
Y1 - 2019/10/1
N2 - In this paper, the probability density functions (PDFs)of scalar stochastic differential equations (SDEs)subject to α-stable Lévy white noise are investigated. The path integral (PI)method is extended to solve one-dimensional space fractional Fokker-Planck-Kolmogorov (FPK)equations, which are the governing equations corresponded to scalar SDEs excited by α-stable Lévy white noise. First, we derive a short time solution of the one-dimensional space fractional FPK equation, which is used in the Chapman-Kolmogorov-Smoluchowski (CKS)equation to obtain the PI solution. Then, the accuracy of the PI solution is analyzed theoretically in terms of its characteristic function. Our results demonstrate that the PI method has a higher accuracy than the first order finite difference method for one step iteration in time. Finally, several illustrative examples are carried out in detail to verify the feasibility and effectiveness of the PI method for solving one-dimensional space fractional FPK equations. We find that the PI solution agrees well with the exact solution or the Monte Carlo one.
AB - In this paper, the probability density functions (PDFs)of scalar stochastic differential equations (SDEs)subject to α-stable Lévy white noise are investigated. The path integral (PI)method is extended to solve one-dimensional space fractional Fokker-Planck-Kolmogorov (FPK)equations, which are the governing equations corresponded to scalar SDEs excited by α-stable Lévy white noise. First, we derive a short time solution of the one-dimensional space fractional FPK equation, which is used in the Chapman-Kolmogorov-Smoluchowski (CKS)equation to obtain the PI solution. Then, the accuracy of the PI solution is analyzed theoretically in terms of its characteristic function. Our results demonstrate that the PI method has a higher accuracy than the first order finite difference method for one step iteration in time. Finally, several illustrative examples are carried out in detail to verify the feasibility and effectiveness of the PI method for solving one-dimensional space fractional FPK equations. We find that the PI solution agrees well with the exact solution or the Monte Carlo one.
KW - Finite difference method
KW - Monte Carlo simulation
KW - Path integral method
KW - Space fractional FPK equation
KW - α-stable Lévy white noise
UR - https://www.scopus.com/pages/publications/85066292320
U2 - 10.1016/j.jcp.2019.05.023
DO - 10.1016/j.jcp.2019.05.023
M3 - 文章
AN - SCOPUS:85066292320
SN - 0021-9991
VL - 394
SP - 41
EP - 55
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -