Sampling and Parameter Estimation for a Second Order Linear System with a Fractional Brownian Motion

2006 ◽  
Author(s):  
T.E. Duncan ◽  
B. Pasik-Duncan
Keyword(s):  
Parameter Estimation ◽  
Brownian Motion ◽  
Linear System ◽  
Fractional Brownian Motion ◽  
Second Order ◽  
Order Linear

scholarly journals Second-order limit laws for occupation times of fractional Brownian motion

2017 ◽  
Vol 54 (2) ◽  
pp. 444-461 ◽  
Author(s):  
Fangjun Xu
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Method Of Moments ◽  
Second Order ◽  
Hurst Index ◽  
Occupation Times ◽  
Limit Laws ◽  
Additive Functionals ◽  
Finite Dimensional ◽  
Functional Version

Abstract We prove a second-order limit law for additive functionals of a d-dimensional fractional Brownian motion with Hurst index H = 1 / d, using the method of moments and extending the Kallianpur–Robbins law, and then give a functional version of this result. That is, we generalize it to the convergence of the finite-dimensional distributions for corresponding stochastic processes.

Drift Parameter Estimation for a Reflected Fractional Brownian Motion Based on its Local Time

2013 ◽  
Vol 50 (02) ◽  
pp. 592-597 ◽  
Author(s):  
Yaozhong Hu ◽  
Chihoon Lee
Keyword(s):  
Parameter Estimation ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Local Time ◽  
Heavy Traffic ◽  
Queueing Systems ◽  
Service Rate ◽  
Time Process ◽  
State Process ◽  
Drift Parameter

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.

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