TY - JOUR
T1 - Stochastic dynamics driven by combined Lévy-Gaussian noise
T2 - Fractional Fokker-Planck-Kolmogorov equation and solution
AU - Zan, Wanrong
AU - Xu, Yong
AU - Kurths, Jürgen
AU - Chechkin, Aleksei V.
AU - Metzler, Ralf
N1 - Publisher Copyright:
© 2020 IOP Publishing Ltd.
PY - 2020/9/25
Y1 - 2020/9/25
N2 - Starting with a stochastic differential equation driven by combined Gaussian and Lévy noise terms we determine the associated fractional Fokker-Planck-Kolmogorov equation (FFPKE). For constant and power-law forms of an external potential we study the interplay of the two noise forms. Particular emphasis is paid on the discussion of sub-and superharmonic external potentials. We derive the probability density function solving the FFPKE and confirm the obtained shapes by numerical simulations. Particular emphasis is also paid to the stationary probability density function in the confining potentials and the question, to which extent the additional Gaussian noise effects changes on the probability density function compared to the pure Lévy noise case.
AB - Starting with a stochastic differential equation driven by combined Gaussian and Lévy noise terms we determine the associated fractional Fokker-Planck-Kolmogorov equation (FFPKE). For constant and power-law forms of an external potential we study the interplay of the two noise forms. Particular emphasis is paid on the discussion of sub-and superharmonic external potentials. We derive the probability density function solving the FFPKE and confirm the obtained shapes by numerical simulations. Particular emphasis is also paid to the stationary probability density function in the confining potentials and the question, to which extent the additional Gaussian noise effects changes on the probability density function compared to the pure Lévy noise case.
KW - finite difference method
KW - fractional Fokker-Planck-Kolmogorovequation
KW - Gaussian white noise
KW - Monte Carlo simulation
KW - stochastic difference equation
KW - α-stable Lévy white noise
UR - http://www.scopus.com/inward/record.url?scp=85090417946&partnerID=8YFLogxK
U2 - 10.1088/1751-8121/aba654
DO - 10.1088/1751-8121/aba654
M3 - 文章
AN - SCOPUS:85090417946
SN - 1751-8113
VL - 53
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 38
M1 - 385001
ER -