Related papers: Hypoelliptic diffusions: discretization, filtering…

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…

We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which is possibly correlated with the returns of the diffusion…

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…

The objective of this article is to study the asymptotic behavior of a new particle filtering approach in the context of hidden Markov models (HMMs). In particular, we develop an algorithm where the latent-state sequence is segmented into…

In this paper, we study a simple correlation-based strategy for estimating the unknown delay and amplitude of a signal based on a small number of noisy, randomly chosen frequency-domain samples. We model the output of this "compressive…

A variety of researchers have successfully obtained the parameters of low dimensional diffusion models using the data that comes out of atomistic simulations. This naturally raises a variety of questions about efficient estimation,…

Diffusion models recently proved to be remarkable priors for Bayesian inverse problems. However, training these models typically requires access to large amounts of clean data, which could prove difficult in some settings. In this work, we…

Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…

This work proposes a decision-making framework for partially observable systems in continuous time with discrete state and action spaces. As optimal decision-making becomes intractable for large state spaces we employ approximation methods…

An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener Chaos decomposition. The result is applied to the nonlinear filtering problem for the time…

Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential…

Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…

Estimating eigenvectors and low-dimensional subspaces is of central importance for numerous problems in statistics, computer science, and applied mathematics. This paper characterizes the behavior of perturbed eigenvectors for a range of…

A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…

Diffusion and flow matching models generate high-fidelity data by simulating paths defined by Ordinary or Stochastic Differential Equations (ODEs/SDEs), starting from a tractable prior distribution. The probability flow ODE formulation…

This paper focuses on the estimation of partially observed branching processes. First, the estimators from a frequentist perspective proposed in the literature are reviewed. The main objective of this paper is to present computational tools…

Partial differential equations with random inputs have become popular models to characterize physical systems with uncertainty coming from, e.g., imprecise measurement and intrinsic randomness. In this paper, we perform asymptotic rare…

This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…

We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by…

We consider systems of slow--fast diffusions with small noise in the slow component. We construct provably logarithmic asymptotically optimal importance schemes for the estimation of rare events based on the moderate deviations principle.…