Related papers: Nonlinear effects within invariance principles

Inertial effects in fluctuations of the work to sustain a system in a nonequilibrium steady state are discussed for a dragged massive Brownian particle model using a path integral approach. We calculate the work distribution function in the…

We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…

We propose discrete random-field models that are based on random partitions of $\mathbb{N}^2$. The covariance structure of each random field is determined by the underlying random partition. Functional central limit theorems are established…

We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central…

We formulate indefinite integration with respect to an irregular function as an algebraic problem and provide a criterion for the existence and uniqueness of a solution. This allows us to define a good notion of integral with respect to…

The theory of rough paths arose from a desire to establish continuity properties of ordinary differential equations involving terms of low regularity. While essentially an analytic theory, its main motivation and applications are in…

Combining fractional calculus and the Rough Path Theory we study the existence and uniqueness of mild solutions to evolutions equations driven by a H\"older continuous function with H\"older exponent in $(1/3,1/2)$. Our stochastic integral…

In this work, we establish a Trotter-Kato type theorem. More precisely, we characterize the convergence in distribution of Feller processes by examining the convergence of their generators. The main novelty lies in providing quantitative…

We obtain multiplicity results for a class of first-order superquadratic Hamiltonian systems and a class of indefinite superquadratic elliptic systems which lead to the study of strongly indefinite functionals. There is no assumption to the…

An approach to generalize any kind of collinear functionals in density functional theory to non-collinear functionals is proposed. This approach, for the very first time, satisfies the correct collinear limit for any kind of functionals,…

In this paper, based on the initiation of the notion of negatively associated random variables under nonlinear probability, a strong limit theorem for weighted sums of random variables within the same frame is achieved without assumptions…

We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be…

In this article, we propose a new method to compute the effective properties of non-linear disordered media. We use the fact that the effective constants can be defined through the minimum of an energy functional. We express this minimum in…

This article presents a weak law of large numbers and a central limit theorem for the scaled realised covariation of a bivariate Brownian semistationary process. The novelty of our results lies in the fact that we derive the suitable…

We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…

We obtain a strong invariance principle for nonconventional sums and applying this result we derive for them a version of the law of iterated logarithm, as well as an almost sure central limit theorem. Among motivations for such results are…

We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration. The theory provides a differential structure which describes the infinitesimal evolution of Wiener functionals at very small…

We consider a system of differential equations in a fast long range dependent random environment and prove a homogenization theorem involving multiple scaling constants. The effective dynamics solves a rough differential equation, which is…

We present the extension of the effective field theory framework to the mildly non-linear scales. The effective field theory approach has been successfully applied to the late time cosmic acceleration phenomenon and it has been shown to be…

We obtain functional central limit theorems for both discrete time expressions of the form $1/\sqrt{N}\sum_{n=1}^{[Nt]}(F(X(q_1(n)),\ldots, X(q_{\ell}(n)))-\bar{F})$ and similar expressions in the continuous time where the sum is replaced…