Related papers: Local Nonuniqueness for Stochastic Transport Equat…

We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition…

The celebrated De Giorgi-Nash-Moser theory ensures that solutions to uniformly elliptic or parabolic PDEs are bounded and H\"older continuous, even with merely bounded measurable coefficients. For parabolic SPDEs with transport noise,…

This work is devoted to non-linear stochastic Schr\"odinger equations with multiplicative fractional noise, where the stochastic integral is defined following the Riemann-Stieljes approach of Z\"ahle. Under the assumptions that the initial…

Stochastic parametrisations of the interactions among disparate scales of motion in fluid convection are often used for estimating prediction uncertainty, which can arise due to inadequate model resolution, or incomplete observations,…

We show existence and uniqueness of invariant measures for SDE of the form \[ dX_t = g(X_t)dt + u(X_t)dt + dW^H_t \] where $W^H$ is a fractional Brownian motion (fBm) with Hurst parameter $H\in (0,\frac{1}{2})$, $u$ is a linearly dispersive…

This paper focuses on a stochastic system identification problem: given time series observations of a stochastic differential equation (SDE) driven by L\'{e}vy $\alpha$-stable noise, estimate the SDE's drift field. For $\alpha$ in the…

During the last decade Optimal Transport had a relevant role in the study of geometry of singular spaces that culminated with the Lott-Sturm-Villani theory. The latter is built on the characterisation of Ricci curvature lower bounds in…

We show that, in one spatial and arbitrary jump dimension, the averaged solution of a Marcustype SPDE with pure jump L\'evy transport noise satisfies a dissipative deterministic equation involving a fractional Laplace-type operator. To this…

The existence and uniqueness of measure-valued solutions to stochastic nonlinear, non-local Fokker-Planck equations is proven. This type of stochastic PDE is shown to arise in the mean field limit of weakly interacting diffusions with…

In this paper we prove well-posedness and stabibility of a class of stochastic delay differential equations with singular drift. Moreover, we show local well-posedness under localized assumptions.

Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…

We establish a Freidlin-Wentzell type large deviation principle (LDP) for a class of stochastic partial differential equations with locally monotone coefficients driven by L\'evy noise. Our results essentially improve a recent work on this…

We establish the existence of infinitely many global and stationary solutions in $C(\mathbb{R};C^{\vartheta})$ space for some $\vartheta>0$ to the three dimensional Euler equations driven by an additive noise. The result is based on a new…

In this article we consider a class of nonlinear integro-differential equations of the form $$\inf_{\tau \in\mathcal{T}} \bigg\{\int_{\mathbb{R}^d} (u(x+y)+u(x-y)-2u(x))\frac{k_{\tau}(x,y)}{|y|^{d+2s}} \,dy+ b_{\tau}(x) \cdot \nabla…

We study a fairly general class of time-homogeneous stochastic evolutions driven by noises that are not white in time. As a consequence, the resulting processes do not have the Markov property. In this setting, we obtain constructive…

We study the zero-noise limit for autonomous, one-dimensional ordinary differential equations with discontinuous right-hand sides. Although the deterministic equation might have infinitely many solutions, we show, under rather general…

SDE's must be solved in the "anti-Ito" sense when their coefficients are independent. While the "noise-induced drift" matters for the sample paths, it is absent in the Fokker-Planck equation, which takes a particularly simple form and is…

In this article we study (possibly degenerate) stochastic differential equations (SDE) with irregular (or discontiuous) coefficients, and prove that under certain conditions on the coefficients, there exists a unique almost everywhere…

Stochastic modelling necessitates an interpretation of noise. In this paper, we describe the loss of deterministically stable behaviour in a fundamental fluid mechanics problem, conditional to whether noise is introduced in the sense of…

This paper deals with collisionless transport equations in bounded open domains $\Omega \subset \R^{d}$ $(d\geq 2)$ with $\mathcal{C}^{1}$ boundary $\partial \Omega $, orthogonally invariant velocity measure $\bm{m}(\d v)$ with support…