Related papers: Increasing Risk: Dynamic Mean-Preserving Spreads

In this paper we consider a diffusion process obtained as a small random perturbation of a dynamical system attracted to a stable equilibrium point. The drift and the diffusive perturbation are assumed to evolve slowly in time. We describe…

This work is concerned with model reduction of stochastic differential equations and builds on the idea of replacing drift and noise coefficients of preselected relevant, e.g. slow variables by their conditional expectations. We extend…

Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…

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 deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi, Luchko, Pagnini (2001)): the first equation considered here is obtained by adding an exponential…

We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…

We show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for…

We construct a class of stochastic differential equations driven by White Gaussian noise sources whose solutions can be drawn from skewed Gaussian probability laws, here referred as skew-Normal diffusion (SKN) processes. The non-Gaussian…

Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underline noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with…

In this paper, we are interested in conditional McKean-Vlasov jump diffusions, which are also termed as McKean-Vlasov stochastic differential equations with jump idiosyncratic noise and jump common noise. As far as conditional McKean-Vlasov…

We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…

Starting from a particle model describing self-propelled particles interacting through nematic alignment, we derive a macroscopic model for the particle density and mean direction of motion. We first propose a mean-field kinetic model of…

We study the propagation of a ``pulled'' front with multiplicative noise that is created by a local perturbation of an unstable state. Unlike a front propagating into a metastable state, where a separation of time scales for sufficiently…

Stochastic processes offer a fundamentally different paradigm of dynamics than deterministic processes, the most prominent example of the latter being Newton's laws of motion. Here, we discuss in a pedagogical manner a simple and…

Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…

Denoising diffusion probabilistic models (DDPM) are a class of generative models which have recently been shown to produce excellent samples. We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods…

We show that two dynamical systems exhibiting very different deterministic behaviours possess very similar stationary distributions when stabilized by a multiplicative Gaussian white noise. We also discuss practical aspects of numerically…

Diffusion Probabilistic Models stand as a critical tool in generative modelling, enabling the generation of complex data distributions. This family of generative models yields record-breaking performance in tasks such as image synthesis,…

A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…

Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural…