Related papers: Parametric Inference for Discretely Observed Subor…
In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…
We study the problem of parameter estimation for a univariate discretely observed ergodic diffusion process given as a solution to a stochastic differential equation. The estimation procedure we propose consists of two steps. In the first…
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…
We propose a novel method for drift estimation of multiscale diffusion processes when a sequence of discrete observations is given. For the Langevin dynamics in a two-scale potential, our approach relies on the eigenvalues and the…
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…
Existing results for the estimation of the L\'evy measure are mostly limited to the onedimensional setting. We apply the spectral method to multidimensional L\'evy processes in order to construct a nonparametric estimator for the…
We consider simulation of spatially one-dimensional space-time fractional diffusion. Whereas in an earlier paper of ours we have developed the basic theory of what we call parametric subordination via three-fold splitting applied to…
We study parametric inference for ergodic diffusion processes with a degenerate diffusion matrix. Existing research focuses on a particular class of hypo-elliptic SDEs, with components split into `rough'/`smooth' and noise from rough…
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 consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…
This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…
To model subsurface flow in uncertain heterogeneous\ fractured media an elliptic equation with a discontinuous stochastic diffusion coefficient - also called random field - may be used. In case of a one-dimensional parameter space, L\'evy…
We consider a 1-dimensional diffusion process X with jumps. The particularity of this model relies in the jumps which are driven by a multidimensional Hawkes process denoted N. This article is dedicated to the study of a nonparametric…
We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…
In this article we consider the estimation of static parameters for partially observed diffusion processes with discrete-time observations over a fixed time interval. In particular, when one only has access to time-discretized solutions of…
We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class…
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 consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We give conditions for the well-posedness and…
This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural…
Multidimensional hypoelliptic diffusions arise naturally in different fields, for example to model neuronal activity. Estimation in those models is complex because of the degenerate structure of the diffusion coefficient. In this paper we…