# Malliavin calculus techniques for local asymptotic mixed normality and their application to degenerate diffusions

@article{Masaaki2020MalliavinCT, title={Malliavin calculus techniques for local asymptotic mixed normality and their application to degenerate diffusions}, author={Fukasawa Masaaki and Teppei Ogihara}, journal={arXiv: Statistics Theory}, year={2020} }

We study sufficient conditions for a local asymptotic mixed normality property of statistical models. We develop a scheme with the $L^2$ regularity condition proposed by Jeganathan [\textit{Sankhya Ser. A} \textbf{44} (1982) 173--212] so that it is applicable to high-frequency observations of stochastic processes. Moreover, by combining with Malliavin calculus techniques by Gobet [\textit{Bernoulli} \textbf{7} (2001) 899--912, 2001], we introduce tractable sufficient conditions for smooth…

## One Citation

### Local Asymptotic Mixed Normality via Transition Density Approximation and an Application to Ergodic Jump-Diffusion Processes

- Mathematics
- 2021

Abstract. We study sufficient conditions for local asymptotic mixed normality. We weaken the sufficient conditions in Theorem 1 of Jeganathan (Sankhyā Ser. A 1982) so that they can be applied to a…

## References

SHOWING 1-10 OF 17 REFERENCES

### LAMN property for hidden processes: The case of integrated diffusions

- Mathematics
- 2008

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 $…

### Local asymptotic mixed normality property for nonsynchronously observed diffusion processes

- Mathematics
- 2015

We prove the local asymptotic mixed normality (LAMN) property for a family of probability measures defined by parametrized diffusion processes with nonsynchronous observations. We assume that…

### Diffusions with measurement errors. I. Local Asymptotic Normality

- Mathematics
- 2001

We consider a diusion process X which is observed at timesi=n for i =0 ; 1;::: ;n, each observation being subject to a measurement error. All errors are independent and centered Gaussian with known…

### A characterization of limiting distributions of regular estimates

- Mathematics
- 1970

SummaryWe consider a sequence of estimates in a sequence of general estimation problems with a k-dimensional parameter. Under certain very general conditions we prove that the limiting distribution…

### Parametric inference for nonsynchronously observed diffusion processes in the presence of market microstructure noise

- MathematicsBernoulli
- 2018

We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study…

### On continuous conditional Gaussian martingales and stable convergence in law

- Sociology
- 1997

© Springer-Verlag, Berlin Heidelberg New York, 1997, tous droits réservés. L’accès aux archives du séminaire de probabilités (Strasbourg) (http://portail. mathdoc.fr/SemProba/) implique l’accord avec…

### Asymptotic Methods In Statistical Decision Theory

- Mathematics
- 1986

1 Experiments-Decision Spaces.- 1 Introduction.- 2 Vector Lattices-L-Spaces-Transitions.- 3 Experiments-Decision Procedures.- 4 A Basic Density Theorem.- 5 Building Experiments from Other Ones.- 6…

### Matrix analysis

- MathematicsStatistical Inference for Engineers and Data Scientists
- 2018

This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications.

### On the estimation of the diffusion coefficient for multi-dimensional diffusion processes

- Mathematics
- 1993

If a diffusion process has a diffusion coefficient which depends on a parameter 9, one can construct consistent sequences of estimators of 03B8 based on the observation of the process at only n…