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Chen, S., Yu, L.P., Ren, J.L., Xie, X., Li, X.P., Xu, Y., Zhao, G.F., Li, P.Z., Yang, F.Q., Ren, Y. and Liaw, P.K. (2016) Self-Similar Random Process and Chaotic Behavior. In Serrated Flow of High Entropy Alloys. Scientific Reports, 6, Article Number: 29798.
https://doi.org/10.1038/srep29798

has been cited by the following article:

• TITLE: One Dimensional Random Motion on Segment with Reflecting Edges and Dependent Increments

  AUTHORS: Gurami Tsitsiashvili

  KEYWORDS: Fractional Brownian Motion, Rate of Convergence, Anomalous Diffusion, Segment with Reflecting Edges

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.6 No.3, March 15, 2018

  ABSTRACT: In previous papers, the author considered the model of anomalous diffusion, defined by stable random process on an interval with reflecting edges. Estimates of the rate convergence of this process distribution to a uniform distribution are constructed. However, recent physical studies require consideration of models of diffusion, defined not only by stable random process with independent increments but multivariate fractional Brownian motion with dependent increments. This task requires the development of special mathematical techniques evaluation of the rate of convergence of the distribution of multivariate Brownian motion in a segment with reflecting boundaries to the limit. In the present work, this technology is developed and a power estimate of the rate of convergence to the limiting uniform distribution is built.