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March 2011 On the return time for a reflected fractional Brownian motion process on the positive orthant
Chihoon Lee
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J. Appl. Probab. 48(1): 145-153 (March 2011). DOI: 10.1239/jap/1300198141

Abstract

We consider a d-dimensional reflected fractional Brownian motion (RFBM) process on the positive orthant S = R+d, with drift r0Rd and Hurst parameter H ∈ (½, 1). Under a natural stability condition on the drift vector r0 and reflection directions, we establish a return time result for the RFBM process Z; that is, for some δ, κ > 0, supxBExB(δ)] < ∞, where B = {xS : |x| ≤ κ} and τB(δ) = inf{t ≥ δ : Z(t) ∈ B}. Similar results are known for reflected processes driven by standard Brownian motions, and our result can be viewed as their FBM counterpart. Our motivation for this study is that RFBM appears as a limiting workload process for fluid queueing network models fed by a large number of heavy-tailed ON/OFF sources in heavy traffic.

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Chihoon Lee. "On the return time for a reflected fractional Brownian motion process on the positive orthant." J. Appl. Probab. 48 (1) 145 - 153, March 2011. https://doi.org/10.1239/jap/1300198141

Information

Published: March 2011
First available in Project Euclid: 15 March 2011

zbMATH: 1216.60032
MathSciNet: MR2809892
Digital Object Identifier: 10.1239/jap/1300198141

Subjects:
Primary: 60G22
Secondary: 60G15, 60G18, 90B18

Rights: Copyright © 2011 Applied Probability Trust

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Vol.48 • No. 1 • March 2011
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