Related papers: C-infinity-regularization by Noise of Singular ODE…
We study pathwise regularization by noise for equations on the plane in the spirit of the framework outlined by Catellier and Gubinelli (Stochastic Process. Appl., 2016). To this end, we extend the notion of non-linear Young equations to a…
Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is necessary to draw conclusions from these data, and it often becomes essential to construct dynamical models using these data. We…
The regularity and characterization of solutions to degenerate, quasilinear SPDE is studied. Our results are two-fold: First, we prove regularity results for solutions to certain degenerate, quasilinear SPDE driven by Lipschitz continuous…
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…
We consider scalar ODE with a power singularity at the origin, regularized by an additive fractional noise. We show that, as the intensity in front of the noise goes to $0$, the solution converges to the extremal solutions to the ODE (which…
In this paper we study a class of stochastic partial differential equations in the whole space $\mathbb{R}^{d}$, with arbitrary dimension $d\geq 1$, driven by a Gaussian noise white in time and correlated in space. The differential operator…
A linear stochastic continuity equation with non-regular coefficients is considered. We prove existence and uniqueness of strong solution, in the probabilistic sense, to the Cauchy problem when the vector field has low regularity, in which…
We study stochastic optimization from a joint continuous-discrete point of view. Starting from a second-order stochastic differential equation interpreted as a noisy accelerated gradient flow, we discretize the dynamics by a fully implicit…
After a general introduction about the regularization by noise phenomenon in the degenerate setting, the first part of this PhD thesis focuses at establishing the Schauder estimates, a useful analytical tool to prove also the well-posedness…
We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. In the…
In this paper we focus on nonlinear SPDEs with singularities included in both drift and noise coefficients, for which the Gelfand-triple argument developed for (local) monotone SPDEs turns out to be invalid. We propose a general framework…
We prove a regularization by noise phenomenon for semilinear SPDEs driven by multiplicative cylindrical Brownian motion and singular diffusion coefficient. The analysis is based on a combination of infinite dimensional generalizations of…
We study existence and uniqueness of solutions to the equation $dX_t=b(X_t)dt + dB_t$, where $b$ is a distribution in some Besov space and $B$ is a fractional Brownian motion with Hurst parameter $H\leqslant 1/2$. First, the equation is…
Consensus based optimization is a derivative-free particles-based method for the solution of global optimization problems. Several versions of the method have been proposed in the literature, and different convergence results have been…
The stabilisation by noise on the boundary of the Chafee-Infante equation with dynamical boundary conditions subject to a multiplicative It\^o noise is studied. In particular, we show that there exists a finite range of noise intensities…
We establish strong uniqueness for a class of degenerate SDEs of weak H{\"o}rmander type under suitable H{\"o}lder regularity conditions for the associated drift term. Our approach relies on the Zvonkin transform which requires to exhibit…
The momentum formulation of the surface quasi-geostrophic equations consists of two nonlinear terms, besides the pressure term, one of which cannot be written in a divergence form. When the anti-divergence operator is applied to such…
We consider the Navier-Stokes equations in vorticity form in $\mathbb{R}^2$ with a white noise forcing term of multiplicative type, whose spatial covariance is not regular enough to apply the It\^o calculus in $L^q$ spaces, $1<q<\infty$. We…
In this article we introduce and analyze a notion of mild solution for a class of non-autonomous parabolic stochastic partial differential equations defined on a bounded open subset $D\subset\mathbb{R}^{d}$ and driven by an…
In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…