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

• 作者: Gurami Tsitsiashvili
• 来源期刊: 应用数学与应用物理(英文)
• 学科: 数学
• 关键词: FRACTIONAL BROWNIAN Motion Rate of Convergence ANOMALOUS Diffusion SEGMENT with Reflecting EDGES
• 年，卷（期）: 2018,（3）
• 页码范围: 488-497
• 页数: 10页
• 分类号: O1

摘要

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.