# Least-squares estimators based on the Adams method for stochastic differential equations with small Lévy noise

@article{Kobayashi2022LeastsquaresEB, title={Least-squares estimators based on the Adams method for stochastic differential equations with small L{\'e}vy noise}, author={Mitsuki Kobayashi and Yasutaka Shimizu}, journal={Japanese Journal of Statistics and Data Science}, year={2022} }

We consider stochastic differential equations (SDEs) driven by small Lévy noise with some unknown parameters, and propose a new type of least squares estimators based on discrete samples from the SDEs. To approximate the increments of a process from the SDEs, we shall use not the usual Euler method, but the Adams method, that is, a well-known numerical approximation of the solution to the ordinary differential equation appearing in the limit of the SDE. We show the consistency of the proposed…

## One Citation

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## References

SHOWING 1-10 OF 18 REFERENCES

### Lévy processes and stochastic calculus, second ed

- Cambridge Studies in Advanced Mathematics,
- 2009

### Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems

- Mathematics
- 2002

The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). The book is divided into four chapters. The…

### Interpolation and approximation. republication, with minor corrections, of the 1963 original, with a new preface and bibliography

- 1975

### Asymptotic statistics, Cambridge Series in Statistical and

- Probabilistic Mathematics,
- 1998

### Numerical methods for ordinary differential equations

- Computer Science
- 2003

This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior undergraduate and graduate courses in numerical analysis, and is an essential resource for research workers in applied mathematics, physics and engineering.

### Maximnm contrast estimation for diffusion processes from discrete observations

- Mathematics
- 1990

We consider a one-dimensional diffusion process (Xt) with drift b{θ&, u) depending on an unknown parameter # and small known diffusion coefficient , s. The sample path is observed at times k△A, =0,…

### Quasi-likelihood analysis for the stochastic differential equation with jumps

- Mathematics
- 2011

In this paper, we consider a multidimensional diffusion process X with jumps whose jump term is driven by a compound Poisson process, and discuss its parametric estimation. We present asymptotic…

### Estimation for Discretely Observed Small Diffusions Based on Approximate Martingale Estimating Functions

- Mathematics
- 2004

Abstract. We consider an asymptotically efficient estimator of the drift parameter for a multi‐dimensional diffusion process with small dispersion parameter ɛ. In the situation where the sample path…

### A Sufficient Condition for Asymptotic Sufficiency of Incomplete Observations of a Diffusion Process

- Mathematics
- 1990

Consider an m-dimensional diffusion process (X t ) with unknown drift and small known variance observed on a time interval [0, T]. We derive here a general condition ensuring the asymptotic…