相关论文: Path-by-path regularization by noise for scalar co…
In the article, Besov-Orlicz regularity of sample paths of stochastic processes that are represented by multiple integrals of order $n\in\mathbb{N}$ is treated. We give sufficient conditions for the considered processes to have paths in the…
We develop a semi-discretization approximation for scalar conservation laws with multiple rough time dependence in inhomogeneous fluxes. The method is based on Brenier's transport-collapse algorithm and uses characteristics defined in the…
Fourier normal ordering \cite{Unt09bis} is a new algorithm to construct explicit rough paths over arbitrary H\"older-continuous multidimensional paths. We apply in this article the Fourier normal ordering ordering algorithm to the…
In this paper we show that solutions of stochastic partial differential equations driven by Brownian motion can be approximated by stochastic partial differential equations forced by pure jump noise/random kicks. Applications to stochastic…
The paper provides results for the stabilization of a spatially uniform equilibrium profile for a scalar conservation law that arises in the study of traffic dynamics under variable speed limit control. Two different control problems are…
Security of oscillatory true random number generators remains not fully understood due to insufficient understanding of complex $1/f^\alpha$ phase noise. To bridge this gap, we introduce fractional Brownian motion as a comprehensive…
We construct solutions to Burgers type equations perturbed by a multiplicative space-time white noise in one space dimension. Due to the roughness of the driving noise, solutions are not regular enough to be amenable to classical methods.…
We present a new path integral method to analyze stochastically perturbed ordinary differential equations with multiple time scales. The objective of this method is to derive from the original system a new stochastic differential equation…
In this article we prove path-by-path uniqueness in the sense of Davie \cite{Davie07} and Shaposhnikov \cite{Shaposhnikov16} for SDE's driven by a fractional Brownian motion with a Hurst parameter $H\in(0,\frac{1}{2})$, uniformly in the…
In this paper, we investigate the averaging principle for a class of semilinear slow-fast partial differential equations driven by finite-dimensional rough multiplicative noise. Specifically, the slow component is driven by a general random…
We present sufficient conditions for finite controlled rho-variation of the covariance of Gaussian processes with stationary increments, based on concavity or convexity of their variance function. The motivation for this type of conditions…
The Langevin equation with multiplicative noise and state-dependent transport coefficient has to be always complemented with the proper interpretation rule of the noise, such as the Ito and Stratonovich conventions. Although the…
We extend path analysis by giving sufficient conditions for computing the partial covariance of two random variables from their covariance. This is specifically done by correcting the covariance with the product of some partial variance…
The goal of this paper is to define and study a notion of fractional Brownian motion on a Lie group. We define it as at the solution of a stochastic differential equation driven by a linear fractional Brownian motion. We show that this…
We show that a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand $g$ can have any prescribed distribution, moreover, we give both necessary and sufficient conditions when random variables can…
A linear stochastic transport equation with non-regular coefficients is considered. Under the same assumption of the deterministic theory, all weak $L^\infty$-solutions are renormalized. But then, if the noise is nondegenerate, uniqueness…
The transport phenomenon(directional movement) of self-propelled Brownian particles moving in a smooth corrugated confined channel is investigated. It is found that large $x$ direction noise intensity should reduce particles directional…
Starting from the construction of a geometric rough path associated with a fractional Brownian motion with Hurst parameter $H\in]{1/4}, {1/2}[$ given by Coutin and Qian (2002), we prove a large deviation principle in the space of geometric…
This work establishes the existence and regularity of random pullback attractors for parabolic partial differential equations with rough nonlinear multiplicative noise under natural assumptions on the coefficients. To this aim, we combine…
We study some functional inequalities satisfied by the distribution of the solution of a stochastic differential equation driven by fractional Brownian motions. Such functional inequalities are obtained through new integration by parts…