Related papers: Skew-Normal Diffusions
In deep latent Gaussian models, the latent variable is generated by a time-inhomogeneous Markov chain, where at each time step we pass the current state through a parametric nonlinear map, such as a feedforward neural net, and add a small…
We consider a stochastic heat equation driven by a space-time white noise and with a singular drift, where a local-time in space appears. The process we study has an explicit invariant measure of Gibbs type, with a non-convex potential. We…
Score-based diffusion models currently constitute the state of the art in continuous generative modeling. These methods are typically formulated via overdamped or underdamped Ornstein--Uhlenbeck-type stochastic differential equations, in…
We consider spatially extended conductance based neuronal models with noise described by a stochastic reaction diffusion equation with additive noise coupled to a control variable with multiplicative noise but no diffusion. We only assume a…
Biochemical signal transduction, a form of molecular communication, can be modeled using graphical Markov channels with input-modulated transition rates. Such channel models are strongly non-Gaussian. In this paper we use a linear noise…
Generating data from discrete distributions is important for a number of application domains including text, tabular data, and genomic data. Several groups have recently used random $k$-satisfiability ($k$-SAT) as a synthetic benchmark for…
Markovian diffusion processes yield a system of conservation laws which couple various conditional expectation values (local moments). Solutions of that closed system of deterministic partial differential equations stand for a regular…
We obtain solutions to conservation laws under any random initial conditions that are described by Gaussian stochastic processes (in some cases discretized). We analyze the generalization of Burgers' equation for a smooth flux function…
We consider a particle, confined to a moving harmonic potential, under the influence of friction and external asymmetric Poissonian shot noise (PSN). We study the fluctuations of the work done to maintain this system in a nonequilibrium…
Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms…
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…
We study stochastic reaction--diffusion equation $$ \partial_tu_t(x)=\frac12 \partial^2_{xx}u_t(x)+b(u_t(x))+\dot{W}_{t}(x), \quad t>0,\, x\in D $$ where $b$ is a generalized function in the Besov space…
Gravitational wave detectors will need optimal signal-processing algorithms to extract weak signals from the detector noise. Most algorithms designed to date are based on the unrealistic assumption that the detector noise may be modeled as…
McDonald and Clerk [Phys.\ Rev.\ Research 5, 033107 (2023)] showed that for linear open quantum systems the Liouvillian spectrum is independent of the noise strength. We first make this noise-independence principle precise in continuous…
We derive a stochastic partial differential equation that describes the fluctuating behaviour of reaction-diffusion systems of N particles, undergoing Markovian, unary reactions. This generalises the work of Dean [J. Phys. A: Math. and…
This paper investigates the well-posedness and small-noise asymptotics of a class of stochastic partial differential equations defined on a bounded domain of $\mathbb{R}^d$, where the diffusion coefficient depends nonlinearly and…
Score-based Generative Models (SGMs) approximate a data distribution by perturbing it with Gaussian noise and subsequently denoising it via a learned reverse diffusion process. These models excel at modeling complex data distributions and…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…
Classical discriminant analysis assumes identically distributed training data, yet in many applications observations are collected over time and the class-conditional distributions drift. This population drift renders stationary classifiers…