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Weighted sums of I.I.D. Random variables attracted to integrals of stable processes
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  • Published: March 1988

Weighted sums of I.I.D. Random variables attracted to integrals of stable processes

  • Yuji Kasahara1 &
  • Makoto Maejima2 

Probability Theory and Related Fields volume 78, pages 75–96 (1988)Cite this article

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Summary

Under the assumption of the convergence of partial sum processesZ n (t) of i.i.d. random variables to an α-stable Lévy processZ(σ)(t), 0<α≦2, the convergence of weighted sums ∫f n (u)dZ n (u) to ∫f(u)dZ (α)(u) is studied. The general convergence result is then applied to examine the domain of attraction of the fractional stable process.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Tsukuba, 305, Tsukuba, Ibaraki, Japan

    Yuji Kasahara

  2. Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, 223, Yokohama, Japan

    Makoto Maejima

Authors
  1. Yuji Kasahara
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  2. Makoto Maejima
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Additional information

Supported in part by Grant-in-Aid for Scientific Research, No. 60740103, Ministry of Education, Science and Culture

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Kasahara, Y., Maejima, M. Weighted sums of I.I.D. Random variables attracted to integrals of stable processes. Probab. Th. Rel. Fields 78, 75–96 (1988). https://doi.org/10.1007/BF00718037

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  • Received: 01 April 1986

  • Revised: 23 November 1987

  • Issue Date: March 1988

  • DOI: https://doi.org/10.1007/BF00718037

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Convergence Result
  • Stable Process
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