TY - JOUR
T1 - Drift parameter estimation for a reflected fractional brownian motion based on its local time
AU - Hu, Yaozhong
AU - Lee, Chihoon
PY - 2013/6
Y1 - 2013/6
N2 - We consider a drift parameter estimation problem when the state process is a reflected fractional Brownian motion (RFBM) with a nonzero drift parameter and the observation is the associated local time process. The RFBM process arises as the key approximating process for queueing systems with long-range dependent and self-similar input processes, where the drift parameter carries the physical meaning of the surplus service rate and plays a central role in the heavy-traffic approximation theory for queueing systems. We study a statistical estimator based on the cumulative local time process and establish its strong consistency and asymptotic normality.
AB - We consider a drift parameter estimation problem when the state process is a reflected fractional Brownian motion (RFBM) with a nonzero drift parameter and the observation is the associated local time process. The RFBM process arises as the key approximating process for queueing systems with long-range dependent and self-similar input processes, where the drift parameter carries the physical meaning of the surplus service rate and plays a central role in the heavy-traffic approximation theory for queueing systems. We study a statistical estimator based on the cumulative local time process and establish its strong consistency and asymptotic normality.
KW - Asymptotic normality
KW - Fractional Brownian motion
KW - Parameter estimation
KW - Queueing model
KW - Reflected process
KW - Strong consistency
UR - http://www.scopus.com/inward/record.url?scp=84879767150&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84879767150&partnerID=8YFLogxK
U2 - 10.1239/jap/1371648963
DO - 10.1239/jap/1371648963
M3 - Article
AN - SCOPUS:84879767150
SN - 0021-9002
VL - 50
SP - 592
EP - 597
JO - Journal of Applied Probability
JF - Journal of Applied Probability
IS - 2
ER -