Related papers: Neural Drift Estimation for Ergodic Diffusions: No…

Concept drift is a major issue that greatly affects the accuracy and reliability of many real-world applications of machine learning. We argue that to tackle concept drift it is important to develop the capacity to describe and analyze it.…

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 setting of multiscale overdamped Langevin stochastic differential equations, and study the problem of learning the drift function of the homogenized dynamics from continuous-time observations of the multiscale system. We…

In this paper, we study central and non-central limit theorems for partial sum of functionals of general stationary Gaussian fields. We apply our result to study drift parameter estimation problems for some stochastic differential equations…

In this paper we consider the nonparametric functional estimation of the drift of Gaussian processes using Paley-Wiener and Karhunen-Lo\`eve expansions. We construct efficient estimators for the drift of such processes, and prove their…

We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…

Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. The delay structure is written as an integral form with respect to a delay measure. Our contrast…

We investigate the problem of estimating the drift parameter from $N$ independent copies of the solution of a stochastic differential equation driven by a multiplicative fractional Brownian noise with Hurst parameter $H\in (1/3,1)$.…

The purpose of this paper is to prove new fine regularity results for nonlocal drift-diffusion equations via pointwise potential estimates. Our analysis requires only minimal assumptions on the divergence free drift term, enabling us to…

We prove the asymptotic normality of the discretized maximum likelihood estimator for the drift parameter in the homogeneous ergodic diffusion model.

We study a least squares estimator for an unknown parameter in the drift coefficient of a path- distribution dependent stochastic differential equation involving a small dispersion parameter epsilon greater than zero. The estimator, based…

In this paper, we consider stochastic versions of three classical growth models given by ordinary differential equations (ODEs). Indeed we use stochastic versions of Von Bertalanffy, Gompertz, and Logistic differential equations as models.…

The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR…

This paper presents a distributed estimator for a deterministic parametric physical field sensed by a homogeneous sensor network and develops a new transformed expression for the Cramer-Rao lower bound (CRLB) on the variance of distributed…

Generating high quality uncertainty estimates for sequential regression, particularly deep recurrent networks, remains a challenging and open problem. Existing approaches often make restrictive assumptions (such as stationarity) yet still…

We consider controlled differential equations and give new estimates for higher order Euler schemes. Our proofs are inspired by recent work of A. M. Davie who considers first and second order schemes. In order to implement the general case…

In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external…

Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…

We consider stationary stochastic dynamical systems evolving on a compact metric space, by perturbing a deterministic dynamics with a random noise, added according to an arbitrary probabilistic distribution. We prove the maximal and…

This paper deals with the drift estimation in linear stochastic evolution equations (with emphasis on linear SPDEs) with additive fractional noise (with Hurst index ranging from 0 to 1) via least-squares procedure. Since the least-squares…