Subordinated Brownian Motion: Last Time the Process Reaches its Supremum

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• 作者：Stergios B. Fotopoulos (1)
  Venkata K. Jandhyala (2)
  Yuxing Luo (1)
  
  1. Department of Finance & Management Science ; Washington State University ; Pullman ; USA
  2. Department of Mathematics ; Washington State University ; Pullman ; WA ; 99164-4746 ; USA
  
• 关键词：Subordinated Brownian motion ; Brownian motion with negative drift ; Wiener ; Hopf factorization ; generalized gamma convolution ; Primary 60J75 ; Secondary 60J65 ; 60G51
• 刊名：Sankhya A
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：77
• 期：1
• 页码：46-64
• 全文大小：432 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistical Theory and Methods
  Statistics Computing and Software
  Statistics
  
• 出版者：Springer India
• ISSN：0976-8378

文摘

The article develops a theory for the last time the subordinated Brownian motion (SBM with negative drift reaches its supremum. The study includes obtaining expressions for the Laplace transform of the last time that the SBM reaches its supremum and also for its density. In the process, we establish that the last time that the SBM reaches its supremum is a member of the generalized gamma convolution (GGC) family. The theoretical results for the general case have been explicitly derived for some well-known subordinators. Numerical investigations show close agreement between the theoretical derivations and empirical computations.