Estimation for stochastic damping hamiltonian systems under partial observation—I. Invariant density

Cattiaux, Patrick; León, J. B.; Prieur, Clémentine

doi:10.1016/j.spa.2013.10.008

Cited by 17 publications

(33 citation statements)

References 10 publications

(20 reference statements)

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“…A prominent example is the large class of stochastic damping Hamiltonian systems, which are also called Langevin equations, describing the motion of a particle subject to potential, dissipative and random forces (Wu, 2001;Cattiaux et al, 2014aCattiaux et al, , b, 2016Comte et al, 2017). In this case a.·/ = U t and A.·/ = −c.V t , U t /U t − ∇P.V t /, for some function c.·/ and where P.·/ is the potential.…”

Section: Introductionmentioning

confidence: 99%

Hypoelliptic Diffusions: Filtering and Inference from Complete and Partial Observations

Ditlevsen

Samson

2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, because of the noise structure, where the noise components of the different co‐ordinates of the multi‐dimensional process operate on different timescales, standard inference tools are ill conditioned. We propose to use a higher order scheme to approximate the likelihood, such that the different timescales are appropriately accounted for. We show consistency and asymptotic normality with non‐typical convergence rates. When only partial observations are available, we embed the approximation in a filtering algorithm for the unobserved co‐ordinates and use this as a building block in a stochastic approximation expectation–maximization algorithm. We illustrate on simulated data from three models: the harmonic oscillator, the FitzHugh–Nagumo model used to model membrane potential evolution in neuroscience and the synaptic inhibition and excitation model used for determination of neuronal synaptic input.

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Section: Introductionmentioning

confidence: 99%

Hypoelliptic Diffusions: Filtering and Inference from Complete and Partial Observations

Ditlevsen

Samson

2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…Here we shall combine finite time approximation results with mixing properties of the process in the spirit of Dedecker and Prieur (2005) and our previous work Cattiaux, Leon and Prieur (2014). Our method extends to non-reflected diffusion processes satisfying some Lyapunov condition as in Mattingly et al (2002) Shardlow et al (2000) Talay (1990), and actually the compact situation we are looking at, introduces more intricacies.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Invariant density estimation for a reflected diffusion using an Euler scheme

Cattiaux

Prieur

León

2017

Monte Carlo Methods and Applications

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Abstract. We give an explicit error bound between the invariant density of an elliptic reflected diffusion in a smooth compact domain and the kernel estimator built on the symmetric Euler scheme introduced in Bossy, Gobet and Talay (2004).Key words : ergodic reflected diffusion process; Euler scheme rate of convergence for large times; discrete approximation for the invariant measure. MSC 2010Primary: 60J60. Secondary: 60H10 Stochastic ordinary differential equations; 37TL40 Invariant measures; 37A25 Ergodicity, mixing, rates of mixing.

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“…Following the proof of Theorem 3.3 in [8], we can prove that the second term in the last equality above is…”

Section: P Cattiaux J R León and C Prieurmentioning

confidence: 92%

“…This leads us to consider a more general estimation taking into account our two [7] and [8] previous articles. However, to get easier computations, we shall only consider here the case when the two coordinates of the process are observed.…”

Section: Fluctuation-dissipation Relation and Langevin Dynamicsmentioning

confidence: 99%

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Estimation for stochastic damping Hamiltonian systems under partial observation. III. Diffusion term

Cattiaux¹,

León²,

Prieur³

2016

Ann. Appl. Probab.

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International audienceThis paper is the third part of our study started with Cattiaux, León and Prieur (2013, 2014). For some ergodic hamiltonian systems we obtained a central limit theorem for a non-parametric estimator of the invariant density (Cattiaux et al., 2014) and of the drift term (Cattiaux et al., 2013), under partial observation (only the positions are observed). Here we obtain similarly a central limit theorem for a non-parametric estimator of the diffusion term

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Estimation for stochastic damping hamiltonian systems under partial observation—I. Invariant density

Cited by 17 publications

References 10 publications

Hypoelliptic Diffusions: Filtering and Inference from Complete and Partial Observations

Hypoelliptic Diffusions: Filtering and Inference from Complete and Partial Observations

Invariant density estimation for a reflected diffusion using an Euler scheme

Estimation for stochastic damping Hamiltonian systems under partial observation. III. Diffusion term

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