TY - JOUR
T1 - A Parameter Estimation Method Using Linear Response Statistics
AU - Harlim, John
AU - Li, Xiantao
AU - Zhang, He
N1 - Publisher Copyright:
© 2017, Springer Science+Business Media New York.
PY - 2017/7/1
Y1 - 2017/7/1
N2 - This paper presents a new parameter estimation method for Itô diffusions such that the resulting model predicts the equilibrium statistics as well as the sensitivities of the underlying system to external disturbances. Our formulation does not require the knowledge of the underlying system, however, we assume that the linear response statistics can be computed via the fluctuation–dissipation theory. The main idea is to fit the model to a finite set of “essential” statistics that is sufficient to approximate the linear response operators. In a series of test problems, we will show the consistency of the proposed method in the sense that if we apply it to estimate the parameters of the underlying model, then we must obtain the true parameters.
AB - This paper presents a new parameter estimation method for Itô diffusions such that the resulting model predicts the equilibrium statistics as well as the sensitivities of the underlying system to external disturbances. Our formulation does not require the knowledge of the underlying system, however, we assume that the linear response statistics can be computed via the fluctuation–dissipation theory. The main idea is to fit the model to a finite set of “essential” statistics that is sufficient to approximate the linear response operators. In a series of test problems, we will show the consistency of the proposed method in the sense that if we apply it to estimate the parameters of the underlying model, then we must obtain the true parameters.
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U2 - 10.1007/s10955-017-1788-9
DO - 10.1007/s10955-017-1788-9
M3 - Article
AN - SCOPUS:85018669777
SN - 0022-4715
VL - 168
SP - 146
EP - 170
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 1
ER -