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The point process approach for fractionally differentiated random walks under heavy traffic

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  • Barbe, Ph.
  • McCormick, W.P.

Abstract

We prove some heavy-traffic limit theorems for some nonstationary linear processes which encompass the fractionally differentiated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a non-Gaussian stable distribution. The results are based on an extension of the point process methodology to linear processes with nonsummable coefficients and make use of a new maximal type inequality.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:12:p:4028-4053
    DOI: 10.1016/j.spa.2012.08.008
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    1. 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.
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