Related papers: Moment estimation for ergodic diffusion processes
We consider the problem of frequency estimation by observations of the periodic diffusion process possesing ergodic properties in two different situations. The first one corresponds to continuously differentiable with respect to parameter…
We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…
A truncated sequential procedure is constructed for estimating the drift coefficient at a given state point based on discrete data of ergodic diffusion process. A nonasymptotic upper bound is obtained for a pointwise absolute error risk.…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
A general theory of efficient estimation for ergodic diffusion processes sampled at high frequency with an infinite time horizon is presented. High frequency sampling is common in many applications, with finance as a prominent example. The…
We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…
We consider the problems of parameter estimation for several models of threshold ergodic diffusion processes in the asymptotics of large samples. These models are the direct continuous time analogues of the well-known in time series…
We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…
We consider parametric estimation for ergodic diffusion processes with noisy sampled data based on the hybrid method, that is, the multi-step estimation with the initial Bayes type estimators. In order to select proper initial values for…
We treat the change point problem in ergodic diffusion processes from discrete observations. Tonaki et al. (2020) proposed adaptive tests for detecting changes in the diffusion and drift parameters in ergodic diffusion models. When any…
In this paper a concentration inequality is proved for the deviation in the ergodic theorem in the case of discrete time observations of diffusion processes. The proof is based on the geometric ergodicity property for diffusion processes.…
We propose a new method of the construction of the asymptotically efficient estimator-processes asymptotically equivalent to the MLE and the same time much more easy to calculate. We suppose that the observed process is ergodic diffusion…
The global estimation problem of the drift function is considered for a large class of ergodic diffusion processes. The unknown drift $S(\cdot)$ is supposed to belong to a nonparametric class of smooth functions of order $k\geq1$, but the…
We consider adaptive maximum-likelihood-type estimators and adaptive Bayes-type ones for discretely observed ergodic diffusion processes with observation noise whose variance is constant. The quasi-likelihood functions for the diffusion and…
We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction and diffusion functions from the path of one single particle in the system. Our estimator is obtained by…
The problem to establish not only the asymptotic distribution results for statistical estimators but also the moment convergence of the estimators has been recognized as an important issue in advanced theories of statistics. One of the main…
In this article, we consider a jump diffusion process (X_t), with drift function b, diffusion coefficient sigma and jump coefficient xi^{2}. This process is observed at discrete times t=0,Delta,...,nDelta. The sampling interval Delta tends…
Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…
We consider parametric inference for an ergodic and stationary diffusion process, when the data are high-frequency observations of the integral of the diffusion process. Such data are obtained via certain measurement devices, or if…
We deal with the change point problem in ergodic diffusion processes based on high frequency data. Tonaki et al. (2020, 2021) studied the change point problem for the ergodic diffusion process model. However, the change point problem for…