Related papers: The killed Brox diffusion
Bulk matter produced in heavy ion collisions has multiple conserved quantum numbers like baryon number, strangeness and electric charge. The diffusion process of these charges can be described by a diffusion matrix describing the…
We consider a single genetic locus which carries two alleles, labelled P and Q. This locus experiences selection and mutation. It is linked to a second neutral locus with recombination rate r. If r=0, this reduces to the study of a single…
We study diffusions, variational principles and associated boundary value problems on directed graphs with natural weightings. Using random walks and exit times, we associate to certain subgraphs (domains) a pair of sequences, each of which…
This paper defines a novel Bayesian inverse problem to infer an infinite-dimensional uncertain operator appearing in a differential equation, whose action on an observable state variable affects its dynamics. Inference is made tractable by…
We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a…
Diffusion models typically operate in the standard framework of generative modelling by producing continuously-valued datapoints. To this end, they rely on a progressive Gaussian smoothing of the original data distribution, which admits an…
A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be…
We propose a stochastic model for intracellular transport processes associated with the activity of molecular motors. This out-of-equilibrium model, based on a generalized Langevin equation, considers a particle immersed in a viscoelastic…
This article is concerned with a mathematical tool, the Associated Transfer Matrix T, which proves useful in the study of a wide class of physical problems involving multilayer heterostructures. General properties of linear, second order…
Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…
We study the properties of the ``Rigid Laplacian'' operator, that is we consider solutions of the Laplacian equation in the presence of fixed truncation errors. The dynamics of convergence to the correct analytical solution displays the…
We consider inference of the parameters of the diffusion term for Cox-Ingersoll-Ross and similar processes with a power type dependence of the diffusion coefficient from the underlying process. We suggest some original pathwise estimates…
Generative models have shown strong generation ability while efficient likelihood estimation is less explored. Energy-based models~(EBMs) define a flexible energy function to parameterize unnormalized densities efficiently but are notorious…
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…
We consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We give conditions for the well-posedness and…
This paper investigates an inverse random source problem for the stochastic fractional Helmholtz equation. The source is modeled as a centered, complex-valued, microlocally isotropic generalized Gaussian random field whose covariance and…
We study the diffusion of tagged hard core interacting particles under the influence of an external force field. Using the Jepsen line we map this many particle problem onto a single particle one. We obtain general equations for the…
Some fractional and anomalous diffusions are driven by equations involving fractional derivatives in both time and space. Such diffusions are processes with randomly varying times. In representing the solutions to those diffusions, the…
Generative diffusion models showed high success in many fields with a powerful theoretical background. They convert the data distribution to noise and remove the noise back to obtain a similar distribution. Many existing reviews focused on…
A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally…