Related papers: Estimation for change point of discretely observed…
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…
We consider the adaptive test for the parameter change in discretely observed ergodic diffusion processes based on the cusum test. Using two test statistics based on the two quasi-log likelihood functions of the diffusion parameter and 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 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 propose a new statistical observation scheme of diffusion processes named convolutional observation, where it is possible to deal with smoother observation than ordinary diffusion processes by considering convolution of diffusion…
We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an…
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…
Given a heterogeneous time-series sample, the objective is to find points in time (called change points) where the probability distribution generating the data has changed. The data are assumed to have been generated by arbitrary unknown…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of 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…
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.…
The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant…
When recording the movement of individual animals, cells or molecules one will often observe changes in their diffusive behaviour at certain points in time along their trajectory. In order to capture the different diffusive modes assembled…
This study explores a Gaussian quasi-likelihood approach for estimating parameters of diffusion processes with Markovian regime switching. Assuming the ergodicity under high-frequency sampling, we will show the asymptotic normality of the…
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…
This paper studies the change point problem for a general parametric, univariate or multivariate family of distributions. An information theoretic procedure is developed which is based on general divergence measures for testing the…
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.…
We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…
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…
Change-point detection methods are proposed for the case of temporary failures, or transient changes, when an unexpected disorder is ultimately followed by a readjustment and return to the initial state. A base distribution of the…