Maximum likelihood estimation for small noise multiscale diffusions

Spiliopoulos, Konstantinos; Chronopoulou, Alexandra

doi:10.1007/s11203-013-9088-8

Cited by 12 publications

(15 citation statements)

References 26 publications

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“…We remark that although convergence of X ε toX is generally expected (see [22,19,20,25]), the statement of Theorem 1 is stronger than what is to be found in the literature of which we are aware. We prove that X ε →X in L p uniformly in t ∈ [0, T ], in the general case in the full Euclidean space, specifying an explicit rate of convergence.…”

Section: Introductionmentioning

confidence: 65%

“…Sufficient conditions for asymptotic normality when δ ≡ 1 (i.e., without multiple scales) appear in [15,16]. In the multiscale setup the only known asymptotic normality results are those of [25]. In [25], the authors study the special case of a multiscale process in which the fast process is simply Y ε = X ε /δ and furthermore assume uniformly bounded coefficients that are also periodic in the fast variable.…”

Section: Asymptotic Normality Of the Mlementioning

confidence: 99%

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Statistical inference for perturbed multiscale dynamical systems

Gailus

Spiliopoulos

2017

Stochastic Processes and their Applications

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We study statistical inference for small-noise-perturbed multiscale dynamical systems. We prove consistency, asymptotic normality, and convergence of all scaled moments of an appropriatelyconstructed maximum likelihood estimator (MLE) for a parameter of interest, identifying precisely its limiting variance. We allow full dependence of coefficients on both slow and fast processes, which take values in the full Euclidean space; coefficients in the equation for the slow process need not be bounded and there is no assumption of periodic dependence. The results provide a theoretical basis for calibration of smallnoise-perturbed multiscale dynamical systems. Data from numerical simulations are presented to illustrate the theory. 1 arXiv:1504.07645v3 [math.PR]

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Section: Introductionmentioning

confidence: 65%

Section: Asymptotic Normality Of the Mlementioning

confidence: 99%

Statistical inference for perturbed multiscale dynamical systems

Gailus

Spiliopoulos

2017

Stochastic Processes and their Applications

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“…Meanwhile, it is shown also in [24] that direct application of the principle of maximum likelihood with discretely-sampled data via Euler-Maruyama approximation produces consistent estimates only if the data is first appropriately subsampled. Most closely related to the present work are [13,31], wherein the authors prove consistency and asymptotic normality of the continuous-data MLE for special cases of (1).…”

Section: Introductionmentioning

confidence: 78%

“…The first statement, (29), follows by the triangle inequality and Theorem 1. (30) may be obtained in the same way by omitting the last term in (31).…”

Section: Appendixmentioning

confidence: 99%

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Discrete-Time Statistical Inference for Multiscale Diffusions

Gailus¹,

Spiliopoulos²

2018

Multiscale Model. Simul.

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We study statistical inference for small-noise-perturbed multiscale dynamical systems under the assumption that we observe a single time series from the slow process only. We construct estimators for both averaging and homogenization regimes, based on an appropriate misspecified model motivated by a second-order stochastic Taylor expansion of the slow process with respect to a function of the time-scale separation parameter. In the case of a fixed number of observations, we establish consistency, asymptotic normality, and asymptotic statistical efficiency of a minimum contrast estimator (MCE), the limiting variance having been identified explicitly; we furthermore establish consistency and asymptotic normality of a simplified minimum constrast estimator (SMCE), which is however not in general efficient. These results are then extended to the case of high-frequency observations under a condition restricting the rate at which the number of observations may grow vis-à-vis the separation of scales. Numerical simulations illustrate the theoretical results.

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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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Maximum likelihood estimation for small noise multiscale diffusions

Cited by 12 publications

References 26 publications

Statistical inference for perturbed multiscale dynamical systems

Statistical inference for perturbed multiscale dynamical systems

Discrete-Time Statistical Inference for Multiscale Diffusions

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

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