# Asymptotic equivalence for pure jump L\'evy processes with unknown L\'evy density and Gaussian white noise

@article{Mariucci2015AsymptoticEF, title={Asymptotic equivalence for pure jump L\'evy processes with unknown L\'evy density and Gaussian white noise}, author={Ester Mariucci}, journal={arXiv: Probability}, year={2015} }

## 8 Citations

Spectral-free estimation of L\'evy densities in high-frequency regime

- Mathematics
- 2017

We construct an estimator of the L\'evy density of a pure jump L\'evy process, possibly of infinite variation, from the discrete observation of one trajectory at high frequency. The novelty of our…

Asymptotic equivalence for density estimation and gaussian white noise: An extension

- Mathematics, Computer Science
- 2015

The aim of this paper is to present an extension of the well-known as-ymptotic equivalence between density estimation experiments and a Gaussian white noise model by enlarging the nonparametric class of the admissible densities.

Compound Poisson approximation to estimate the Lévy density

- Mathematics
- 2017

We construct an estimator of the Levy density, with respect to the Lebesgue measure, of a pure jump Levy process from high frequency observations: we observe one trajectory of the Levy process over…

Efficient nonparametric inference for discretely observed compound Poisson processes

- Mathematics
- 2015

A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and Lévy distributions are proposed and functional…

Classical robots perturbed by Lévy processes: analysis and Lévy disturbance rejection methods

- Mathematics
- 2017

The stability and convergence of state, disturbance and parametric estimates of a robot have been analyzed using the Lyapunov method in the existing literature. In this paper, we analyze the problem…

Strong Gaussian approximation of the mixture Rasch model

- Computer Science, MathematicsBernoulli
- 2019

It is proved that the mixture Rasch model is asymptotically equivalent to a Gaussian observation scheme in Le Cam's sense as n tends to infinity and m is allowed to increase slowly in n.

of the Bernoulli Society for Mathematical Statistics and Probability Volume Twenty Seven Number Four November 2021

- Mathematics
- 2021

The papers published in Bernoulli are indexed or abstracted in Current Index to Statistics, Mathematical Reviews, Statistical Theory and Method Abstracts-Zentralblatt (STMA-Z), and Zentralblatt für…

of the Bernoulli Society for Mathematical Statistics and Probability Volume Twenty Five Number Two May 2019

- 2019

## References

SHOWING 1-10 OF 53 REFERENCES

Asymptotic equivalence for inhomogeneous jump diffusion processes and white noise

- Mathematics
- 2015

We prove the global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a time inhomogeneous jump-diffusion process and a…

Estimation for L\'{e}vy processes from high frequency data within a long time interval

- Mathematics
- 2011

In this paper, we study nonparametric estimation of the L\'{e}vy density for L\'{e}vy processes, with and without Brownian component. For this, we consider $n$ discrete time observations with step…

Asymptotic equivalence of jumps Lévy processes and their discrete counterpart

- Mathematics
- 2013

We establish the global asymptotic equivalence between a pure jumps Levy process $\{X_t\}$ on the time interval $[0,T]$ with unknown Levy measure $\nu$ belonging to a non-parametric class and the…

Asymptotic equivalence for nonparametric regression with non-regular errors

- Mathematics
- 2011

Asymptotic equivalence in Le Cam’s sense for nonparametric regression experiments is extended to the case of non-regular error densities, which have jump discontinuities at their endpoints. We prove…

On the asymptotic equivalence and rate of convergence of nonparametric regression and Gaussian white noise

- Mathematics
- 2004

The experiments of nonparametric regression with equidistant design points and Gaussian white noise are considered. Brown and Low have proven asymptotic equivalence of these models under a quite…

Asymptotic equivalence of functional linear regression and a white noise inverse problem

- Mathematics
- 2011

We consider the statistical experiment of functional linear regression (FLR). Furthermore, we introduce a white noise model where one observes an Ito process, which contains the covariance operator…

Asymptotic Equivalence of Density Estimation and Gaussian White Noise

- Mathematics, Computer Science
- 1996

It is shown that an i.i.d. sample of size n with density f is globally asymptotically equivalent to a white noise experiment with drift f l/2 and variance 1/4n -l .

Asymptotic equivalence for nonparametric generalized linear models

- Mathematics
- 1998

Summary. We establish that a non-Gaussian nonparametric regression model is asymptotically equivalent to a regression model with Gaussian noise. The approximation is in the sense of Le Cam's…

Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift

- Mathematics
- 2004

This paper establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This…

Asymptotic equivalence of nonparametric diffusion and Euler scheme experiments

- Mathematics
- 2014

The main goal of the asymptotic equivalence theory of Le Cam (1986) is to approximate general statistical models by simple ones. We develop here a global asymptotic equivalence result for…