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

Ph. Barbe and W.P. McCormick

Stochastic Processes and their Applications, 2012, vol. 122, issue 12, 4028-4053

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.

Keywords: Heavy traffic; Point process; Supremum functional; Fractional random walk; FARIMA process; Poisson process (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spa.2012.08.008

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