TY - JOUR
T1 - On the return time for a reflected fractional Brownian motion process on the positive orthant
AU - Lee, Chihoon
PY - 2011/3
Y1 - 2011/3
N2 - We consider a d-dimensional reflected fractional Brownian motion (RFBM) process on the positive orthant S = ℝ+d, with drift r0 ∈ ℝd and Hurst parameter H ∈ (1/2, 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, supx∈B Ex [τB(δ)] < ∞, where B = {x ∈ S : |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.
AB - We consider a d-dimensional reflected fractional Brownian motion (RFBM) process on the positive orthant S = ℝ+d, with drift r0 ∈ ℝd and Hurst parameter H ∈ (1/2, 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, supx∈B Ex [τB(δ)] < ∞, where B = {x ∈ S : |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.
KW - Heavy traffic theory
KW - Reflected fractional Brownian motion
KW - Return time
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U2 - 10.1239/jap/1300198141
DO - 10.1239/jap/1300198141
M3 - Article
AN - SCOPUS:80054768654
SN - 0021-9002
VL - 48
SP - 145
EP - 153
JO - Journal of Applied Probability
JF - Journal of Applied Probability
IS - 1
ER -