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Tempered Fractional Stable Motion

Author

Listed:
  • Mark M. Meerschaert

    (Michigan State University)

  • Farzad Sabzikar

    (Michigan State University)

Abstract

Tempered fractional stable motion adds an exponential tempering to the power-law kernel in a linear fractional stable motion, or a shift to the power-law filter in a harmonizable fractional stable motion. Increments from a stationary time series that can exhibit semi-long-range dependence. This paper develops the basic theory of tempered fractional stable processes, including dependence structure, sample path behavior, local times, and local nondeterminism.

Suggested Citation

  • Mark M. Meerschaert & Farzad Sabzikar, 2016. "Tempered Fractional Stable Motion," Journal of Theoretical Probability, Springer, vol. 29(2), pages 681-706, June.
  • Handle: RePEc:spr:jotpro:v:29:y:2016:i:2:d:10.1007_s10959-014-0585-5
    DOI: 10.1007/s10959-014-0585-5
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    References listed on IDEAS

    as
    1. Dozzi, Marco & Shevchenko, Georgiy, 2011. "Real harmonizable multifractional stable process and its local properties," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1509-1523, July.
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    Cited by:

    1. Ehsan Azmoodeh & Yuliya Mishura & Farzad Sabzikar, 2022. "How Does Tempering Affect the Local and Global Properties of Fractional Brownian Motion?," Journal of Theoretical Probability, Springer, vol. 35(1), pages 484-527, March.

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