Related papers: Increasing Risk: Dynamic Mean-Preserving Spreads

Noisy dynamical models are employed to describe a wide range of phenomena. Since exact modeling of these phenomena requires access to their microscopic dynamics, whose time scales are typically much shorter than the observable time scales,…

Discrete diffusion models, like continuous diffusion models, generate high-quality samples by gradually undoing noise applied to datapoints with a Markov process. Gradual generation in theory comes with many conceptual benefits; for…

We study a stochastic spatial epidemic model where the $N$ individuals carry two features: a position and an infection state, interact and move in $\R^d$. In this Markovian model, the evolution of the infection states are described with the…

We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…

Score-based diffusion models generate samples from an unknown target distribution using a time-reversed diffusion process. While such models represent state-of-the-art approaches in industrial applications such as artificial image…

For a wide class of continuous-time Markov processes, including all irreducible hypoelliptic diffusions evolving on an open, connected subset of $\RL^d$, the following are shown to be equivalent: (i) The process satisfies (a slightly weaker…

Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…

The emerging diffusive dynamics in many complex systems shows a characteristic crossover behaviour from anomalous to normal diffusion which is otherwise fitted by two independent power-laws. A prominent example for a subdiffusive-diffusive…

Diffusion models have attracted a lot of attention in recent years. These models view speech generation as a continuous-time process. For efficient training, this process is typically restricted to additive Gaussian noising, which is…

Turbulent flows posses broadband, power-law spectra in which multiscale interactions couple high-wavenumber fluctuations to large-scale dynamics. Although diffusion-based generative models offer a principled probabilistic forecasting…

We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…

We explore unsupervised speech enhancement using diffusion models as expressive generative priors for clean speech. Existing approaches guide the reverse diffusion process using noisy speech through an approximate, noise-perturbed…

The dynamics of short-lived mRNA results in bursts of protein production in gene regulatory networks. We investigate the propagation of bursting noise between different levels of mathematical modelling, and demonstrate that conventional…

A quantitatively reliable theoretical description of the dynamics of fluctuations in non-equilibrium is indispensable in the experimental search for the QCD critical point by means of ultra-relativistic heavy-ion collisions. In this work we…

We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics.…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the…

The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…

We study mean-field inclusion processes with an additional slow phase, in which particle interactions occur at a vanishing rate proportional to the inverse system size. In the thermodynamic limit, such systems exhibit condensation at high…

A moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established. The main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random…