On Random Flights with Non-uniformly Distributed Directions

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• 作者：Alessandro De Gregorio (1) alessandro.degregorio@uniroma1.it
• 关键词：Bessel functions – ; Dirichlet distributions – ; Hyperspherical coordinates – ; Non ; isotropic random motions – ; Non ; uniform distributions on the sphere
• 刊名：Journal of Statistical Physics
• 出版年：2012
• 出版时间：April 2012
• 年：2012
• 卷：147
• 期：2
• 页码：382-411
• 全文大小：959.8 KB
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• 作者单位：1. Dipartimento di Scienze Statistiche, 鈥淪apienza鈥?University of Rome, P.le Aldo Moro 5, 00185 Rome, Italy
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Statistical Physics
  Mathematical and Computational Physics
  Physical Chemistry
  Quantum Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9613

文摘

This paper deals with a new class of random flights in ℝ d , d≥2, characterized by non-uniform probability distributions on the multidimensional sphere. These random motions differ from similar models appeared in literature where the directions are taken according to the uniform law. The family of angular probability distributions introduced in this paper depends on a parameter ν≥0, which gives the anisotropy of the motion. Furthermore, we assume that the number of changes of direction performed by the random flight is fixed. The time lengths between two consecutive changes of orientation have joint probability distribution given by a Dirichlet density function.