• Corpus ID: 251371477

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… 

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

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.

References

SHOWING 1-10 OF 44 REFERENCES

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

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.

Optimal convergence rates for the invariant density estimation of jump-diffusion processes

We aim at estimating the invariant density associated to a stochastic differential equation with jumps in low dimension, which is for d = 1 and d = 2. We consider a class of jump diffusion processes

Minimax rate of estimation for invariant densities associated to continuous stochastic differential equations over anisotropic Holder classes

We study the problem of the nonparametric estimation for the density π of the stationary distribution of a d -dimensional stochastic differential equation ( X t ) t ∈ [0 ,T ] . From the continuous

On estimating the diffusion coefficient from discrete observations

This paper is concerned with the problem of estimation for the diffusion coefficient of a diffusion process on R, in a non-parametric situation. The drift function can be unknown and considered as a

Adaptive invariant density estimation for ergodic diffusions over anisotropic classes

Consider some multivariate diffusion process X = (Xt)t≥0 with unique invariant probability measure and associated invariant density ρ, and assume that a continuous record of observations X =

LAMN property for hidden processes: The case of integrated diffusions

In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process $X$. Our data are given by $

Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions

The problem of determining a periodic Lipschitz vector field $b=(b_1, \dots, b_d)$ from an observed trajectory of the solution $(X_t: 0 \le t \le T)$ of the multi-dimensional stochastic differential

Nonparametric estimation for interacting particle systems: McKean–Vlasov models

We consider a system of N interacting particles, governed by transport and diffusion, that converges in a mean-field limit to the solution of a McKean–Vlasov equation. From the observation of a

Averaging along irregular curves and regularisation of ODEs