Related papers: Quasi-likelihood analysis of an ergodic diffusion …

We consider the classical estimation problem of an unknown drift parameter within classes of nondegenerate diffusion processes. Using rough path theory (in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE) with…

This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…

We study small perturbations of diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of hypersurfaces. Each surface is assumed to be repelling for the unperturbed process, and the unperturbed motion on each of the…

Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…

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…

Suppose we observe a geometrically ergodic semi-Markov process and have a parametric model for the transition distribution of the embedded Markov chain, for the conditional distribution of the inter-arrival times, or for both. The first two…

A continuous-time regression model with a jointly strictly sub-Gaussian random noise is considered in the paper. Upper exponential bounds for probabilities of large deviations of the least squares estimator for the regression parameter are…

For a fixed $T$ and $k \geq 2$, a $k$-dimensional vector stochastic differential equation $dX_t=\mu(X_t, \theta)dt+\nu(X_t)dW_t,$ is studied over a time interval $[0,T]$. Vector of drift parameters $\theta$ is unknown. The dependence in…

We consider statistical inference for a class of continuous semimartingale regression models based on high-frequency observations subject to contamination by finite-activity jumps and spike noise. By employing density-power weighting and…

This paper studies an approximation method for the log-likelihood function of a nonlinear diffusion process using the bridge of the diffusion. The main result (Theorem \refthm:approx) shows that this approximation converges uniformly to the…

Invariant ergodic measures for generalized Boole type transformations are studied using an invariant quasi-measure generating function approach based on special solutions to the Frobenius--Perron operator. New two-dimensional Boole type…

The variance of noise plays an important role in many change-point detection procedures and the associated inferences. Most commonly used variance estimators require strong assumptions on the true mean structure or normality of the error…

This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…

This paper studies the quasi-maximum-likelihood estimator (QMLE) in a general conditionally heteroscedastic time series model of multiplicative form $X_t=\sigma_tZ_t$, where the unobservable volatility $\sigma_t$ is a parametric function of…

This paper investigates the quasi-maximum likelihood inference including estimation, model selection and diagnostic checking for linear double autoregressive (DAR) models, where all asymptotic properties are established under only…

We establish the convergence rates and asymptotic distributions of the common break change-point estimators, obtained by least squares and maximum likelihood in panel data models and compare their asymptotic variances. Our model assumptions…

Latent variable models have been widely applied in different fields of research in which the constructs of interest are not directly observable, so that one or more latent variables are required to reduce the complexity of the data. In…

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…

We extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically…

The paper considers an Euler discretization based numerical scheme for approximating functionals of invariant distribution of an ergodic diffusion. Convergence of the numerical scheme is shown for suitably chosen discretization step, and a…