48 research outputs found
On drift parameter estimation for mean-reversion type stochastic differential equations with discrete observations
We study the parameter estimation for mean-reversion type stochastic differential equations driven by Brownian motion. The equations, involving a small dispersion parameter, are observed at discrete (regularly spaced) time instants. The least square method is utilized to derive an asymptotically consistent estimator. Discussions on the rate of convergence of the least square estimator are presented. The new feature of this study is that, due to the mean-reversion type drift coefficient in the stochastic differential equations, we have to use the Girsanov transformation to simplify the equations, which then gives rise to the corresponding convergence of the least square estimator being with respect to a family of probability measures indexed by the dispersion parameter, while in the literature the existing results have dealt with convergence with respect to a given probability measure
Asymptotic equivalence of discretely observed diffusion processes and their Euler scheme: small variance case
This paper establishes the global asymptotic equivalence, in the sense of the
Le Cam -distance, between scalar diffusion models with unknown drift
function and small variance on the one side, and nonparametric autoregressive
models on the other side. The time horizon is kept fixed and both the cases
of discrete and continuous observation of the path are treated. We allow non
constant diffusion coefficient, bounded but possibly tending to zero. The
asymptotic equivalences are established by constructing explicit equivalence
mappings.Comment: 21 page
Small noise asymptotics of the glr test for off-line change detection in misspecified diffusion processes
Minimum distance parameter estimation for a stochastic equation with additive fractional Brownian sheet
Self-normalized asymptotic properties for the parameter estimation in fractional Ornstein–Uhlenbeck process
Frequency Domain Estimation of Integrated Volatility for Itô Processes in the Presence of Market-Microstructure Noise
Maximum likelihood estimation for doubly stochastic poisson processes with partial observations
On Empirical Processes for Ergodic Diffusions and Rates of Convergence of "M"-estimators
This paper contributes to the development of empirical process theory for ergodic diffusions. We prove an entropy-type maximal inequality for the increments of the empirical process of an ergodic diffusion. The inequality is used to study the rate of convergence of "M"-estimators. Copyright 2003 Board of the Foundation of the Scandinavian Journal of Statistics..