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Decomposition of self-similar stable mixed moving averages
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  • Published: July 2002

Decomposition of self-similar stable mixed moving averages

  • Vladas Pipiras 1 &
  • Murad S. Taqqu1 

Probability Theory and Related Fields volume 123, pages 412–452 (2002)Cite this article

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  • 19 Citations

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Abstract.

 Let α? (1,2) and X α be a symmetric α-stable (S α S) process with stationary increments given by the mixed moving average

where is a standard Lebesgue space, is some measurable function and M α is a SαS random measure on X ×ℝ with the control measure m α (dx, du) = μ(dx)du. We show that if X α is self-similar, then it is determined by a nonsingular flow, a related cocycle and a semi-additive functional. By using the Hopf decomposition of the flow into its dissipative and conservative components, we establish a unique decomposition in distribution of X α into two independent processes

where the process X α D is determined by a nonsingular dissipative flow and the process X α C is determined by a nonsingular conservative flow. In this decomposition, the linear fractional stable motion, for example, is determined by a conservative flow.

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Authors and Affiliations

  1. Department of Mathematics, Boston University, 111 Cummington St., Boston, MA 02215, USA. e-mail: pipiras@math.bu.edu, murad@math.bu.edu, , , , , , US

    Vladas Pipiras  & Murad S. Taqqu

Authors
  1. Vladas Pipiras
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  2. Murad S. Taqqu
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Received: 20 June 2000 / Revised version: 6 September 2001 / Published online: 14 June 2002

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Pipiras , V., Taqqu, M. Decomposition of self-similar stable mixed moving averages. Probab Theory Relat Fields 123, 412–452 (2002). https://doi.org/10.1007/s004400200196

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  • Issue Date: July 2002

  • DOI: https://doi.org/10.1007/s004400200196

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Keywords

  • Control Measure
  • Measurable Function
  • Moving Average
  • Random Measure
  • Lebesgue Space
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