Regular Article - Statistical and Nonlinear Physics
Asymmetric space–time correlated continuous-time random walk
Department of Physics, Beijing Technology and Business University, 100048, Beijing, China
2 Institute of System Science, Beijing Technology and Business University, 100048, Beijing, China
Accepted: 22 May 2023
Published online: 4 June 2023
In this manuscript, we present an asymmetric space–time correlated continuous-time random walk model. The waiting time distribution is considered to follow a power law with , whereas the jump lengths are governed by a pair of asymmetric time-correlated conditional Gaussian-like distributions. The diffusive behaviors are analyzed and discussed by calculating the variance of the displacement analytically and numerically. Results reveal that the space–time correlation and the asymmetry can yield quite nontrivial anomalous diffusive behaviors: for , the diffusion presents a bi-fractional form, and for , it displays a multi-fractional one. However, after experiencing a crossover caused by all diffusive terms at intermediate timescales, the diffusion always evolves towards a steady state that is characterized by the term with the largest diffusion exponent at large timescales.
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