Eigenfunction martingale estimating functions and filtered data for drift estimation of discretely observed multiscale diffusions

Abdulle, Assyr; Pavliotis, Grigorios A.; Zanoni, Andrea

doi:10.1007/s11222-022-10081-7

Cited by 7 publications

(2 citation statements)

References 34 publications

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“…In [24] and in the series of works [16,17], the authors develop the theory of this class of spectral estimators for single-scale SDEs, which is further applied to the multiscale case in [18]. Recently, the technique based on filtered data of [3] has been combined with eigenfuction martingale estimating functions for inferring effective dynamics from discrete-time data from the full model in [5].…”

Section: Literature Reviewmentioning

confidence: 99%

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Robust estimation of effective diffusions from multiscale data

Garegnani

Zanoni

2023

Communications in Mathematical Sciences

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We present a novel methodology based on filtered data and moving averages for estimating effective dynamics from observations of multiscale systems. We show in a semi-parametric framework of the Langevin type that our approach is asymptotically unbiased with respect to the theory of homogenization. Moreover, we demonstrate on a range of challenging numerical experiments that our method is accurate in extracting coarse-grained dynamics from multiscale data. In particular, the estimators we propose are more robust and require less knowledge of the full model than the standard technique of subsampling, which is widely employed in practice in this setting.

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Section: Literature Reviewmentioning

confidence: 99%

“…The proof of Theorems 2.1 to 2.3 is obtained by applying techniques similar to the ones employed in [3,5,39], and is presented in detail in Section 4.…”

Section: Theorem 23mentioning

confidence: 99%

Robust estimation of effective diffusions from multiscale data

Garegnani

Zanoni

2023

Communications in Mathematical Sciences

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Drift Estimation of Multiscale Diffusions Based on Filtered Data

et al. 2021

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We study the problem of drift estimation for two-scale continuous time series. We set ourselves in the framework of overdamped Langevin equations, for which a single-scale surrogate homogenized equation exists. In this setting, estimating the drift coefficient of the homogenized equation requires pre-processing of the data, often in the form of subsampling; this is because the two-scale equation and the homogenized single-scale equation are incompatible at small scales, generating mutually singular measures on the path space. We avoid subsampling and work instead with filtered data, found by application of an appropriate kernel function, and compute maximum likelihood estimators based on the filtered process. We show that the estimators we propose are asymptotically unbiased and demonstrate numerically the advantages of our method with respect to subsampling. Finally, we show how our filtered data methodology can be combined with Bayesian techniques and provide a full uncertainty quantification of the inference procedure.

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Eigenfunction martingale estimating functions and filtered data for drift estimation of discretely observed multiscale diffusions

2022

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We propose a novel method for drift estimation of multiscale diffusion processes when a sequence of discrete observations is given. For the Langevin dynamics in a two-scale potential, our approach relies on the eigenvalues and the eigenfunctions of the homogenized dynamics. Our first estimator is derived from a martingale estimating function of the generator of the homogenized diffusion process. However, the unbiasedness of the estimator depends on the rate with which the observations are sampled. We therefore introduce a second estimator which relies also on filtering the data, and we prove that it is asymptotically unbiased independently of the sampling rate. A series of numerical experiments illustrate the reliability and efficiency of our different estimators.

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Eigenfunction martingale estimating functions and filtered data for drift estimation of discretely observed multiscale diffusions

Cited by 7 publications

References 34 publications

Robust estimation of effective diffusions from multiscale data

Robust estimation of effective diffusions from multiscale data

Drift Estimation of Multiscale Diffusions Based on Filtered Data

Eigenfunction martingale estimating functions and filtered data for drift estimation of discretely observed multiscale diffusions

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