Related papers: Weak invariance principle in Besov spaces for stat…

We introduce the concept of stochastic measure-valued solutions to the complete Euler system describing the motion of a compressible inviscid fluid subject to stochastic forcing, where the nonlinear terms are described by defect measures.…

A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and…

This work concerns about multiscale multivalued McKean-Vlasov stochastic systems. First of all, we use a contractive mapping principle to establish the well-posedness for fully coupled multivalued McKean-Vlasov stochastic systems under…

We study Markov processes associated with stochastic differential equations, whose non-linearities are gradients of convex functionals. We prove a general result of existence of such Markov processes and a priori estimates on the transition…

We study large deviation properties of systems of weakly interacting particles modeled by It\^{o} stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures…

Using an alternative notion of entropy introduced by Datta, the max-entropy, we present a new simplified framework to study the minimizers of the specific free energy for random fields which are weakly dependent in the sense of Lewis,…

This work provides some general theorems about unconditional and conditional weak convergence of empirical processes in the case of Poisson sampling designs. The theorems presented in this work are stronger than previously published…

We investigate the existence of weak solutions to a certain system of partial differential equations, modelling the behaviour of a compressible non-Newtonian fluid for small Reynolds number. We construct the weak solutions despite the lack…

Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and…

This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the…

In this work we recast the collisional Vlasov-Maxwell and Vlasov-Poisson equations as systems of coupled stochastic and partial differential equations, and we derive stochastic variational principles which underlie such reformulations. We…

Firstly, we invoke the weak convergence (resp. strong convergence) of translated basic methods involving nonexpansive operators to establish the weak convergence (resp. strong convergence) of the associated method with both perturbation and…

In this paper some general theory is presented for locally stationary processes based on the stationary approximation and the stationary derivative. Laws of large numbers, central limit theorems as well as deterministic and stochastic bias…

Stolarsky's invariance principle quantifies the deviation of a subset of a metric space from the uniform distribution. Classically derived for spherical sets, it has been recently studied in a number of other situations, revealing a general…

The existence of weak solutions is established for stochastic Volterra equations with time-inhomogeneous coefficients allowing for general kernels in the drift and convolutional or bounded kernels in the diffusion term. The presented…

We prove a new Donsker's invariance principle for independent and identically distributed random variables under the sub-linear expectation. As applications, the small deviations and Chung's law of the iterated logarithm are obtained.

This work is devoted to averaging principle of a two-time-scale stochastic partial differential equation on a bounded interval $[0, l]$, where both the fast and slow components are directly perturbed by additive noises. Under some regular…

In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and non irreducible Markov chains…

We develop a "weak Wa\.zewski principle" for discrete and continuous time dynamical systems on metric spaces having a weaker topology to show that attractors can be continued in a weak sense. After showing that the Wasserstein space of a…

The conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but…