https://doi.org/10.1140/epjb/s10051-023-00544-9
Regular Article - Statistical and Nonlinear Physics
Asymmetric space–time correlated continuous-time random walk
1
Department of Physics, Beijing Technology and Business University, 100048, Beijing, China
2
Institute of System Science, Beijing Technology and Business University, 100048, Beijing, China
Received:
22
March
2023
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.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjb/s10051-023-00544-9.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
