TY - JOUR

T1 - A Parameter Estimation Method Using Linear Response Statistics

AU - Harlim, John

AU - Li, Xiantao

AU - Zhang, He

N1 - Funding Information:
The research of JH and XL was supported by the NSF Grant DMS-1619661. JH also acknowledges supports from DMS-1317919, ONR Grant N00014-16-1-2888 and ONR MURI Grant N00014-12-1-0912. XL also acknowledges support from NSF Grant DMS-1522617. HZ was partially supported as a GRA under the NSF Grant DMS-1317919.

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.

UR - http://www.scopus.com/inward/record.url?scp=85018669777&partnerID=8YFLogxK

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U2 - 10.1007/s10955-017-1788-9

DO - 10.1007/s10955-017-1788-9

M3 - Article

AN - SCOPUS:85018669777

VL - 168

SP - 146

EP - 170

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1

ER -