Related papers: Modeling and Analysis of Switching Diffusion Syste…
We propose a deterministic denoising algorithm for discrete-state diffusion models. The key idea is to derandomize the generative reverse Markov chain by introducing a variant of the herding algorithm, which induces deterministic state…
Diffusion models have emerged as a powerful framework for generative tasks in deep learning. They decompose generative modeling into two computational primitives: deterministic neural-network evaluation and stochastic sampling. Current…
A novel model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution…
Diffusion models have demonstrated exceptional performances in various fields of generative modeling, but suffer from slow sampling speed due to their iterative nature. While this issue is being addressed in continuous domains, discrete…
We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing…
We study the existence and uniqueness of rank-based interacting systems of stochastic differential equations. These systems can be seen as modifications with state-dependent coefficients of the Atlas model in mathematical finance. The…
Systems are studied in which transport is possible due to large extension with open boundaries in certain directions but the particles responsible for transport can disappear from it by leaving it in other directions, by chemical reaction…
Let M be a compact connected oriented Riemannian manifold. The purpose of this paper is to investigate the long time behavior of a degenerate stochastic differential equation on the state space $M\times \mathbb{R}^{n}$; which is obtained…
We study the steady state of a stochastic particle system on a two-dimensional lattice, with particle influx, diffusion and desorption, and the formation of a dimer when particles meet. Surface processes are thermally activated, with…
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a diffusion with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued function. We establish…
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…
We formulate a data-driven method for constructing finite volume discretizations of a dynamical system's underlying Continuity / Fokker-Planck equation. A method is employed that allows for flexibility in partitioning state space,…
Stochastic dynamics of several systems can be modeled via piecewise deterministic time evolution of the state, interspersed by random discrete events. Within this general class of systems, we consider time-triggered stochastic hybrid…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
When studying out-of-equilibrium systems, one often excites the dynamics in some degrees of freedom while removing the excitation in others through damping. In order for the system to converge to a statistical steady state, the dynamics…
We propose a class of non-Markov population models with continuous or discrete state space via a limiting procedure involving sequences of rescaled and randomly time-changed Galton--Watson processes. The class includes as specific cases the…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- direct cascading or fragmentation, spatial dynamics, and external driving -- are combined in a classical age-dependent…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…