Related papers: Coarse-graining and fluctuations: Two birds with o…
For Markov processes evolving on multiple time-scales a combination of large component scalings and averaging of rapid fluctuations can lead to useful limits for model approximation. A general approach to proving a law of large numbers to a…
Large and moderate deviation principles are proved for Engel continued fractions, a new type of continued fraction expansion with non-decreasing partial quotients in number theory.
In this paper we discuss the connections between a Vlasov-Fokker-Planck equation and an underlying microscopic particle system, and we interpret those connections in the context of the GENERIC framework (\"Ottinger 2005). This…
Based on a nonsmooth coherence condition, we construct and prove the convergence of a forward-backward splitting method that alternates between steps on a fine and a coarse grid. Our focus is a total variation regularised inverse imaging…
We present a simple model to account for the rheological behavior observed in recent experiments on micellar gels. The model combines attachment-detachment kinetics with stretching due to shear, and shows well-defined jammed and flowing…
We examine two basic assumptions of kinetic theory-- binary collisions and molecular chaos-- using numerical simulations of sheared granular materials. We investigate a wide range of densities and restitution coefficients and demonstrate…
Advances in statistical learning theory have resulted in a multitude of different designs of learning machines. But which ones are implemented by brains and other biological information processors? We analyze how various abstract Bayesian…
Motivated by the wide range of applicability of the fluctuation and dissipation phenomena in non-equilibrium systems, we provide a universal study scheme for the dissipation of the energy and the corresponding Brownian motion analysis of…
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…
The link between Tauberian theorems and large deviations is surveyed, with particular reference to regular variation.
For a fractional Brownian motion $B^H$ with Hurst parameter $H\in]{1/4},{1/2}[\cup]{1/2},1[$, multiple indefinite integrals on a simplex are constructed and the regularity of their sample paths are studied. Then, it is proved that the…
Using the Naimark dilation theory we investigate the question under what conditions an observable which is a coarse graining of another observable is a function of it. To this end, conditions for the separability and for the Boolean…
This work explores the manner in which classical phase space distribution functions converge to the microcanonical distribution. We first prove a theorem about the lack of convergence, then define a generalization of the coarse-graining…
Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. In the context of molecular simulation, standard…
We consider some possible approaches to the fractional-order generalization of definition of variation (functional) derivative. Some problems of formulation of a fractional-order variational derivative are discussed. To give a consistent…
Given a fine-scale physical theory characterized by an evolutionary system of equations and a set of quantities, defined from the variables of the fine theory, that serve as a coarse representation of the fine scale phenomena, a systematic…
In this short note we consider semi-Markov processes satisfying the condition of direction-time independence (Markov renewal processes). We derive large deviation principles and fluctuation theorems for the empirical current and the…
The existing fractional grey prediction models mainly use discrete fractional-order difference and accumulation, but in the actual modeling, continuous fractional-order calculus has been proved to have many excellent properties, such as…
After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to…
We prove a large deviation principle for stochastic differential equations driven by semimartingales, with additive controls. Conditions are given in terms of characteristics of driven semimartingales, so that if the noise-control pairs…