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On simulation and properties of the stable law

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Abstract

The stable distribution, in its many parametrizations, is central to many stochastic processes. Many random variables that occur in the study of Lévy processes are related to it. Good progress has been made recently for simulating various quantities related to the stable law. In this note, we survey exact random variate generators for these distributions. Many distributional identities are also reviewed.

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Acknowledgments

We thank the referee for his thorough and helpful report.

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Authors and Affiliations

  1. School of Computer Science, McGill University, 3480 University Street, Montreal, H3A 2K6, Canada

    Luc Devroye

  2. Department of Information and Systems Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

    Lancelot James

Authors
  1. Luc Devroye
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  2. Lancelot James
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Correspondence to Luc Devroye.

Additional information

The first author was sponsored by NSERC Grant A3456. The second author was supported by (General Research Fund) GRF-601712 of the Hong Kong SAR.

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Devroye, L., James, L. On simulation and properties of the stable law. Stat Methods Appl 23, 307–343 (2014). https://doi.org/10.1007/s10260-014-0260-0

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