Related papers: Unbiased Parameter Estimation of Partially Observe…

This paper is the third part of our study started with Cattiaux, Le\'{o}n and Prieur [Stochastic Process. Appl. 124 (2014) 1236-1260; ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014) 359-384]. For some ergodic Hamiltonian systems, we obtained…

In this paper, we consider static parameter estimation for a class of continuous-time state-space models. Our goal is to obtain an unbiased estimate of the gradient of the log-likelihood (score function), which is an estimate that is…

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…

Let X be the mild solution to a semilinear stochastic partial differential equation. In this article, we develop methodology to sample from the infinite-dimensional diffusion bridge that arises from conditioning X on a linear transformation…

We consider statistical inference in factor analysis for ergodic and non-ergodic diffusion processes from discrete observations. Factor model based on high frequency time series data has been mainly discussed in the field of high…

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 develop and analyze a class of unbiased Monte Carlo estimators for multivariate jump-diffusion processes with state-dependent drift, volatility, jump intensity and jump size. A change of measure argument is used to extend existing…

This paper presents a nonparametric statistical modeling method for quantifying uncertainty in stochastic gradient systems with isotropic diffusion. The central idea is to apply the diffusion maps algorithm to a training data set to produce…

Traditionally, systems governed by linear Partial Differential Equations (PDEs) are spatially discretized to exploit their algebraic structure and reduce the computational effort for controlling them. Due to beneficial insights of the PDEs,…

We introduce a nonparametric model for inferring time-evolving, unobserved probability distributions from discrete-time data consisting of unlabelled partitions. The latent process is a two-parameter Poisson-Dirichlet diffusion, and…

Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of…

Diffusion bridge models in both continuous and discrete state spaces have recently become powerful tools in the field of generative modeling. In this work, we leverage the discrete state space formulation of bridge matching models to…

We present a method to downscale idealized geophysical fluid simulations using generative models based on diffusion maps. By analyzing the Fourier spectra of images drawn from different data distributions, we show how one can chain together…

A general method is proposed which allows one to estimate drift and diffusion coefficients of a stochastic process governed by a Langevin equation. It extends a previously devised approach [R. Friedrich et al., Physics Letters A 271, 217…

We consider the filtering of continuous-time finite-state hidden Markov models, where the rate and observation matrices depend on unknown time-dependent parameters, for which no prior or stochastic model is available. We quantify and…

We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…

Simulation of conditioned diffusion processes is an essential tool in inference for stochastic processes, data imputation, generative modelling, and geometric statistics. Whilst simulating diffusion bridge processes is already difficult on…

The purpose of the present work is to construct estimators for the random effects in a fractional diffusion model using a hybrid estimation method where we combine parametric and nonparametric thechniques. We precisely consider $n$…

We study a distributed node-specific parameter estimation problem where each node in a wireless sensor network is interested in the simultaneous estimation of different vectors of parameters that can be of local interest, of common interest…

Spreading processes are often modelled as a stochastic dynamics occurring on top of a given network with edge weights corresponding to the transmission probabilities. Knowledge of veracious transmission probabilities is essential for…