Related papers: Finite dimensional systems with random external fi…
The traditional wave equation models wave propagation in an ideal conducting medium. For characterizing the wave propagation in inhomogeneous media with frequency dependent power-law attenuation, the space-time fractional wave equation…
The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order…
We develop a complete and rigorous mathematical framework for the analysis of stochastic neural field equations under the influence of spatially extended additive noise. By comparing a solution to a fixed deterministic front profile it is…
We consider systems of interacting particles which are described by a second order Langevin equation. The class of equations considered includes the situation where the particle evolution is governed by Hamiltonian dynamics with additional…
Many systems in nature and laboratories are far from equilibrium and exhibit significant fluctuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
It is shown that evolution of an open quantum system can be exactly described in terms of wave function which obeys Schrodinger equation with randomly varying parameters whose statistics is universally determined by separate dynamics of the…
A process-theoretic approach to electrodynamics based on persistent Kac-type stochastic processes is developed. Finite-velocity stochastic propagation is taken as primary, while relativistic wave equations arise as emergent descriptions…
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics like work, heat and entropy production to the level of individual trajectories of well-defined…
A stochastic treatment yielding to the derivation of a general Fokker-Planck equation is presented to model the slow convergence towards equilibrium of mean-field systems due to finite-N effects. The thermalization process involves notably…
Recently two generalized nonlinear Schr\"{o}dinger equations have been proposed by Chavanis [Eur. Phys. J. Plus 132 (2017) 286] by applying Nottale's theory of scale relativity relying on a fractal space-time to describe dissipation in…
In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…
This paper presents a novel approach for propagating uncertainties in dynamical systems building on high-order Taylor expansions of the flow and moment-generating functions (MGFs). Unlike prior methods that focus on Gaussian distributions,…
We consider the response of a dynamical system driven by external adiabatic fluctuations. Based on the `adiabatic following approximation' we have made a systematic separation of time-scales to carry out an expansion in $\alpha |\mu|^{-1}$,…
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…
Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…
In this article, the existence and uniqueness about the solution for a class of stochastic fractional-order differential equation systems are investigated, where the fractional derivative is described in Caputo sense. The fractional…
We study the Fluctuation Theorem (FT) for entropy production in chaotic discrete-time dynamical systems on compact metric spaces, and extend it to empirical measures, all continuous potentials, and all weak Gibbs states. In particular, we…
In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters $H_{1}, H_{2}…
We develop a general formalism for introducing stochastic fluctuations around thermodynamic equilibrium which takes into account, for the first time, recent developments on the causality and stability properties of relativistic hydrodynamic…