Related papers: Measure-valued affine and polynomial diffusions

Variable order space-fractional diffusion equation derived as an important model to describe complex anomalous diffusion phenomenon. In this article, well-posedness theory has been constructed for equations with the "Dirichlet" or the…

In this paper, we are concerned with long-time behavior of Euler-Maruyama schemes associated with a range of regime-switching diffusion processes. The key contributions of this paper lie in that existence and uniqueness of numerical…

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…

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

Diffusion models (DMs) have recently emerged as SoTA tools for generative modeling in various domains. Standard DMs can be viewed as an instantiation of hierarchical variational autoencoders (VAEs) where the latent variables are inferred…

The definition of infinite dimensional Fresnel integrals is generalized to the case of polynomial phase functions of any degree and applied to the construction of a functional integral representation of the solution of a general class of…

Measures generated by Iterated Function Systems composed of uncountably many one--dimensional affine maps are studied. We present numerical techniques as well as rigorous results that establish whether these measures are absolutely or…

We propose a framework to perform Bayesian inference using conditional score-based diffusion models to solve a class of inverse problems in mechanics involving the inference of a specimen's spatially varying material properties from noisy…

When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…

We consider diffusion of independent molecules in an insulated Euclidean domain with unknown diffusivity parameter. At a random time and position, the molecules may bind and stop diffusing in dependence of a given `binding potential'. The…

In this paper we consider the continuous--time nonlinear filtering problem, which has an infinite--dimensional solution in general, as proved by Chaleyat--Maurel and Michel. There are few examples of nonlinear systems for which the optimal…

Using appropriate power series evaluations, we determine all moments of arbitrary positive powers of the arcsine. As consequences we evaluate several doubly infinite classes of power series involving central binomial coefficients and…

This paper proposes a novel diffusion-index model for forecasting when predictors are high-dimensional matrix-valued time series. We apply an $\alpha$-PCA method to extract low-dimensional matrix factors and build a bilinear regression…

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…

We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the…

We classify valuations on lattice polygons with values in the ring of formal power series that commute with the action of the affine unimodular group. A typical example of such valuations is induced by the Laplace transform, but as it turns…

We present a general Bayesian formalism for the definition of Figures of Merit (FoMs) quantifying the scientific return of a future experiment. We introduce two new FoMs for future experiments based on their model selection capabilities,…

The paper is devoted to a study of phase transitions in the Hermitian random matrix models with a polynomial potential. In an alternative equivalent language, we study families of equilibrium measures on the real line in a polynomial…

Momentum diffusion is a possible mechanism for driving macroscopic quantum systems towards classical behaviour. Experimental tests of this hypothesis rely on a precise estimation of the strength of this diffusion. We show that…

Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic…