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Heavy-traffic approximations for fractionally integrated random walks in the domain of attraction of a non-Gaussian stable distribution

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  • Barbe, Ph.
  • McCormick, W.P.

Abstract

We prove some heavy-traffic limit theorems for processes which encompass the fractionally integrated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a non-Gaussian stable distribution.

Suggested Citation

  • Barbe, Ph. & McCormick, W.P., 2012. "Heavy-traffic approximations for fractionally integrated random walks in the domain of attraction of a non-Gaussian stable distribution," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1276-1303.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:4:p:1276-1303
    DOI: 10.1016/j.spa.2012.01.008
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    References listed on IDEAS

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    1. Dieker, A.B., 2005. "Conditional limit theorems for queues with Gaussian input, a weak convergence approach," Stochastic Processes and their Applications, Elsevier, vol. 115(5), pages 849-873, May.
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    Cited by:

    1. Barbe, Ph. & McCormick, W.P., 2012. "The point process approach for fractionally differentiated random walks under heavy traffic," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 4028-4053.

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