# Malliavin calculus for the optimal estimation of the invariant density of discretely observed diffusions in intermediate regime

@inproceedings{Amorino2022MalliavinCF, title={Malliavin calculus for the optimal estimation of the invariant density of discretely observed diffusions in intermediate regime}, author={Chiara Amorino and Arnaud Gloter}, year={2022} }

Let ( X t ) t ≥ 0 be solution of a one-dimensional stochastic diﬀerential equation. Our aim is to study the convergence rate for the estimation of the invariant density in intermediate regime, assuming that a discrete observation of the process ( X t ) t ∈ [0 ,T ] is available, when T tends to ∞ . We ﬁnd the convergence rates associated to the kernel density estimator we proposed and a condition on the discretization step ∆ n which plays the role of threshold between the intermediate regime and…

## One Citation

### Estimation of the invariant density for discretely observed diffusion processes: impact of the sampling and of the asynchronicity

- Mathematics, Computer Science
- 2022

A kernel density estimator is proposed and its convergence rates for the pointwise estimation of the invariant density under anisotropic H¨older smoothness constraints are studied and it is exhibited that the non synchronicity of the data introduces additional bias terms in the study of the estimator.

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A kernel density estimator is proposed and its convergence rates for the pointwise estimation of the invariant density under anisotropic H¨older smoothness constraints are studied and it is exhibited that the non synchronicity of the data introduces additional bias terms in the study of the estimator.

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