Related papers: Efficient drift parameter estimation for ergodic s…
Within the nonparametric diffusion model, we develop a multiple test to infer about similarity of an unknown drift $b$ to some reference drift $b_0$: At prescribed significance, we simultaneously identify those regions where violation from…
In this paper, we investigate the problem of strong approximation of the solutions of stochastic differential equations (SDEs) when the drift coefficient is given in integral form. We investigate its upper error bounds, in terms of the…
We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…
We study the nonparametric Nadaraya-Watson estimator of the drift function for ergodic stochastic processes driven by fractional Brownian motion of Hurst parameter H > 1/2. The estimator is based on the discretely observed stochastic…
Penalized estimation methods for diffusion processes and dependent data have recently gained significant attention due to their effectiveness in handling high-dimensional stochastic systems. In this work, we introduce an adaptive…
We refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed level, yet at this level (threshold) its coefficients can be…
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…
The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift,…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…
We study statistical inference of the drift parameters for the Volterra Ornstein-Uhlenbeck process on R in the ergodic regime. For continuous-time observations, we derive the corresponding maximum likelihood estimators and show that they…
In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation…
The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…
This paper is devoted to the estimation of the shift parameter in a semiparametric regression model when the distribution of the observation times is unknown. Hence, we propose to use a stochastic algorithm which takes into account the…
Statistical inference for stochastic processes has advanced significantly due to applications in diverse fields, but challenges remain in high-dimensional settings where parameters are allowed to grow with the sample size. This paper…
In this article we study (possibly degenerate) stochastic differential equations (SDE) with irregular (or discontiuous) coefficients, and prove that under certain conditions on the coefficients, there exists a unique almost everywhere…
We study a class of ergodic BSDEs related to PDEs with Neumann boundary conditions. The randomness of the drift is given by a forward process under weakly dissipative assumptions with an invertible and bounded diffusion matrix. Furthermore,…
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 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…
A non-parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non-parametric function that will be estimated by two methods. On one hand, we propose a locally linear estimator…