Related papers: Approximate filtering via discrete dual processes

This paper uses the generator approach of Stein's method to analyze the gap between steady-state distributions of Markov chains and diffusion processes. Until now, the standard way to invoke Stein's method for this problem was to use the…

We consider an extended birth-death-immigration process defined on a lattice formed by the integers of $d$ semiaxes joined at the origin. When the process reaches the origin, then it may jumps toward any semiaxis with the same rate. The…

Diffusion models for continuous state spaces based on Gaussian noising processes are now relatively well understood from both practical and theoretical perspectives. In contrast, results for diffusion models on discrete state spaces remain…

We address the problem of approximating the posterior probability distribution of the fixed parameters of a state-space dynamical system using a sequential Monte Carlo method. The proposed approach relies on a nested structure that employs…

Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…

Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…

We study the dynamics of diffusion processes acting on directed multiplex networks, i.e., coupled multilayer networks where at least one layer consists of a directed graph. We reveal that directed multiplex networks may exhibit a faster…

Regime-switching processes contain two components: continuous component and discrete component, which can be used to describe a continuous dynamical system in a random environment. Such processes have many different properties than general…

We introduce a new class of nonparametric prior distributions on the space of continuously varying densities, induced by Dirichlet process mixtures which diffuse in time. These select time-indexed random functions without jumps, whose…

To model discrete sequences such as DNA, proteins, and language using diffusion, practitioners must choose between three major methods: diffusion in discrete space, Gaussian diffusion in Euclidean space, or diffusion on the simplex. Despite…

A two-types, discrete-time population model with finite, constant size is constructed, allowing for a general form of frequency-dependent selection and skewed offspring distribution. Selection is defined based on the idea that individuals…

Let us consider a pair signal-observation ((xn,yn),n 0) where the unobserved signal (xn) is a Markov chain and the observed component is such that, given the whole sequence (xn), the random variables (yn) are independent and the conditional…

A new application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, we here employ numerical solutions of the dual processes…

This paper contributes to the emerging viewpoint that governing equations for dynamic state estimation, conditioned on the history of noisy measurements, can be viewed as gradient flow on the manifold of joint probability density functions…

This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob's $h$-transforms that are typically intractable.…

Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook…

Denoising diffusion probabilistic models and score-matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on…

Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…

Donsker Theorem is perhaps the most famous invariance principle result for Markov processes. It states that when properly normalized, a random walk behaves asymptotically like a Brownian motion. This approach can be extended to general…

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…