相关论文: Local Nonuniqueness for Stochastic Transport Equat…
We prove pathwise uniqueness for stochastic differential equations driven by non-degenerate symmetric $\alpha$-stable L\'evy processes with values in $\R^d$ having a bounded and $\beta$-H\"older continuous drift term. We assume $\beta > 1 -…
We investigate the existence of periodic solutions for a class of nonlocal continuity equations, which include mean-field equations derived from systems of coupled oscillators. While periodic solutions at the particle level have been…
In this article we introduce a new method for the construction of unique strong solutions of a larger class of stochastic delay equations driven by a discontinuous drift vector field and a Wiener process. The results obtained in this paper…
The purpose of this paper is to study some properties of solutions to one dimensional as well as multidimensional stochastic differential equations (SDEs in short) with super-linear growth conditions on the coefficients. Taking inspiration…
We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish $L^2$ stability and convergence of the difference approximations under conditions that are less strict than those required…
We establish transportation cost inequalities, with respect to the uniform and $L_2$-metric, on the path space of continuous functions, for laws of solutions of stochastic differential equations with reflections. We also consider the case…
Based on a compactness criterion for random fields in Wiener-Sobolev spaces, in this paper, we prove the unique strong solvability of time-inhomogeneous stochastic differential equations with drift coefficients in critical Lebesgue spaces,…
We prove uniqueness in law for possibly degenerate SDEs having a linear part in the drift term. Diffusion coefficients corresponding to non-degenerate directions of the noise are assumed to be continuous. When the diffusion part is constant…
Ergodicity for local and nonlocal stochastic singular $p$-Laplace equations is proven, without restriction on the spatial dimension and for all $p\in[1,2)$. This generalizes previous results from [Gess, T\"{o}lle; J. Math. Pures Appl.,…
We investigate the existence and regularity of the local times of the solution to a linear system of stochastic wave equations driven by a Gaussian noise that is fractional in time and colored in space. Using Fourier analytic methods, we…
We provide sufficient conditions on the coefficients of a stochastic functional differential equation with bounded memory driven by Brownian motion which guarantee existence and uniqueness of a maximal local and global strong solution for…
We give a new result on the well-posedness of the two-dimensional Stochastic Harmonic Map flow, whose study is motivated by the Landau-Lifshitz-Gilbert model for thermal fluctuations in micromagnetics. We construct strong solutions that…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
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…
This paper establishes a quantitative stability theory for one-dimensional stochastic differential equations (SDEs) with non-zero drift, driven by a symmetric $\alpha$-stable process for $\alpha\in(1,2)$. Our work generalizes the classical…
In this work, we extend existing well-posedness by noise results for the stochastic transport and continuity equations by treating them as special cases of the linear advection equation of $k$-forms, which arises naturally in geometric…
In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity…
We introduce a local non-determinism condition for Volterra It\^{o} processes that captures smoothing properties of possibly degenerate noise. By combining the stochastic sewing lemma with one-step Euler approximations, we first prove the…
This paper deals with the drift estimation in linear stochastic evolution equations (with emphasis on linear SPDEs) with additive fractional noise (with Hurst index ranging from 0 to 1) via least-squares procedure. Since the least-squares…
We consider a generalization of classical results of Freidlin and Wentzell to the case of time dependent dissipative drifts. We show the convergence of diffusions with multiplicative noise in the zero limit of a diffusivity parameter to the…