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Reflected Symmetric α-Stable Processes and Regional Fractional Laplacian
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  • Published: 29 December 2005

Reflected Symmetric α-Stable Processes and Regional Fractional Laplacian

  • Qing-Yang Guan1 &
  • Zhi-Ming Ma1 

Probability Theory and Related Fields volume 134, pages 649–694 (2006)Cite this article

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Abstract

In this paper we investigate the reflected symmetric α-stable processes and their generators. We show that the generators are regional fractional Laplacians on the closed region. In the case of 1≤α<2 their existence requires that on the boundary. Among other things we obtain the integration by parts formula of the regional fractional Laplacian and the semi-martingale decomposition of the reflected symmetric α-stable processes.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, China, 100080

    Qing-Yang Guan & Zhi-Ming Ma

Authors
  1. Qing-Yang Guan
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  2. Zhi-Ming Ma
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Corresponding author

Correspondence to Qing-Yang Guan.

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Cite this article

Guan, QY., Ma, ZM. Reflected Symmetric α-Stable Processes and Regional Fractional Laplacian. Probab. Theory Relat. Fields 134, 649–694 (2006). https://doi.org/10.1007/s00440-005-0438-3

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  • Received: 30 May 2004

  • Revised: 26 January 2005

  • Published: 29 December 2005

  • Issue Date: April 2006

  • DOI: https://doi.org/10.1007/s00440-005-0438-3

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Mathematics Subject Classification (2000)

  • Primary 60G52
  • Secondary 60J35
  • 60J75
  • 31C25

Key words or phrases

  • Reflected symmetric α-stable process
  • Regional fractional Laplacian
  • Integration by parts formula
  • Semi-martingale decomposition
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