Related papers: Inference for ergodic diffusions plus noise
In this paper, we address high-dimensional parametric estimation of the drift function in diffusion models, specifically focusing on a $d$-dimensional ergodic diffusion process observed at discrete time points. We consider both a general…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
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…
In this paper, we address a model selection problem for ergodic jump diffusion processes based on high-frequency samples. We evaluate the expected genuine log-likelihood function and derive an Akaike-type information criterion based on the…
In this paper we consider the issue of reliability of measurements in distributed adaptive estimation problem. To this aim, we assume a sensor network with different observation noise variance among the sensors and propose new estimation…
For n-dimensional ergodic diffusion processes with values in $G=\mathbb{R}_{+}^n$ we prove time-independent upper bounds for the transitional density and so also for the unique ergodic density. We do not require geodesic completeness of the…
We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…
We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular…
In this article, we consider a jump diffusion process (X_t)observed at discrete times t=0,Delta,...,nDelta. The sampling interval Delta tends to 0 and nDelta tends to infinity. We assume that (X_t) is ergodic, strictly stationary and…
Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations…
The aim of this paper is to introduce a new type of test statistic for simple null hypothesis on one-dimensional ergodic diffusion processes sampled at discrete times. We deal with a quasi-likelihood approach for stochastic differential…
We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on…
Generative models that maximize model likelihood have gained traction in many practical settings. Among them, perturbation based approaches underpin many strong likelihood estimation models, yet they often face slow convergence and limited…
We consider the problem of the construction of the Goodness-of-Fit test in the case of continuous time observations of a diffusion process with small noise. The null hypothesis is parametric and we use a minimum distance estimator of the…
Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a…
We consider parametric estimation of the continuous part of a class of ergodic diffusions with jumps based on high-frequency samples. Various papers previously proposed threshold based methods, which enable us to distinguish whether…
We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…
The behaviour of many dynamic real phenomena shows different phases, with each one following a sigmoidal type pattern. This requires studying sigmoidal curves with more than one inflection point. In this work, a diffusion process is…
We present a method to infer the arbitrary space-dependent drift and diffusion of a nonlinear stochastic model driven by multiplicative fractional Gaussian noise from a single trajectory. Our method, fractional Onsager-Machlup optimisation…
A goodness of fit test for the drift coefficient of an ergodic diffusion process is presented. The test is based on the score marked empirical process. The weak convergence of the proposed test statistic is studied under the null hypotheses…