Related papers: Diffusion For Ensembles of Standard Maps
In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile…
The authors present a method of indicator random processes, applicable to constructing models of jump processes associated with diffusion process. Indicator random processes are processes that take only two values: 1 and 0, in accordance…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
We study the dynamics of a class of two dimensional stochastic processes, depending on two parameters, which may be interpreted as two different temperatures, respectively associated to interfacial and to bulk noise. Special lines in the…
Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…
We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…
Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stochastic interacting particle systems via tools from information…
Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
We study the limit of a kinetic evolution equation involving a small parameter and perturbed by a smooth random term which also involves the small parameter. Generalizing the classical method of perturbed test functions, we show the…
Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…
We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic…
Exploring chaotic systems via Poincar\'e sections has proven essential in dynamical systems, yet measuring their characteristics poses challenges to identify the various dynamical regimes considered. In this paper, we propose a new approach…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…
Denoising diffusion probabilistic models and score-matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…