Related papers: Large Rank-Based Models with Common Noise
We consider SDEs driven by two different sources of additive noise, which we refer to as intrinsic and common. We establish almost sure existence and uniqueness of pullback attractors with respect to realisations of the common noise only.…
Stochastic partial differential equations driven by Poisson random measures (PRM) have been proposed as models for many different physical systems, where they are viewed as a refinement of a corresponding noiseless partial differential…
This paper is concerned with the problem of regularization by noise of systems of reaction-diffusion equations with mass control. It is known that $\textit{strong}$ solutions to such systems of PDEs may blow-up in finite time. Moreover, for…
We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them…
Power-law noises abound in nature and have been observed extensively in both time series and spatially varying environmental parameters. Although, recent years have seen the extension of traditional stochastic partial differential equations…
We prove pathwise convergence of the layerwise evolution of tokens in a finite-depth, finite-width transformer model with MultiLayer Perceptron (MLP) blocks to a continuous-time stochastic interacting particle system. We also identify the…
The purpose of the present paper consists in proposing and discussing a doubly probabilistic representation for a stochastic porous media equation in the whole space R^1 perturbed by a multiplicative coloured noise. For almost all random…
Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is…
We aim at studying a novel mathematical model associated to a physical phenomenon of infiltration in an homogeneous porous medium. The particularities of our system are connected to the presence of a gravitational acceleration term…
We establish a central limit theorem and large deviations principle that characterises small noise fluctuations of the generalised Dean--Kawasaki stochastic PDE. The fluctuations agree to first order with fluctuations of certain interacting…
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,…
We consider a porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion.…
We study in this paper the longtime behavior of some large but finite populations of interacting stochastic differential equations whose (infinite population) limit Fokker-Planck PDE admits a stable periodic solution. We show that the…
The purpose of the present paper consists in proposing and discussing a double probabilistic representation for a porous media equation in the whole space perturbed by a multiplicative colored noise. For almost all random realizations…
We study multiplicative SDEs perturbed by an additive fractional Brownian motion on another probability space. Provided the Hurst parameter is chosen in a specified regime, we establish existence of probabilistically weak solutions to the…
We study the role of fluctuations in particle systems modeled by Dean-Kawasaki-type equations, which describe the evolution of particle densities in systems with Brownian motion. By comparing microscopic simulations, stochastic partial…
We study the large deviation behavior of a system of diffusing particles with a mean field interaction, described through a collection of stochastic differential equations, in which each particle is driven by a vanishing independent…
We study small noise large deviation asymptotics for stochastic differential equations with a multiplicative noise given as a fractional Brownian motion $B^H$ with Hurst parameter $H>\frac12$. The solutions of the stochastic differential…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
In this paper, we study a stochastic parabolic problem involving a nonlocal diffusion operator associated with nonlocal Robin-type boundary conditions. The stochastic dynamics under consideration are driven by a mixture of a classical…