Related papers: Sharp pathwise nonuniqueness for additive SDEs

In the pathwise stochastic calculus framework, the paper deals with the general study of equations driven by an additive Gaussian noise, with a drift function having an infinite limit at point zero. An ergodic theorem and the convergence of…

We consider a stochastic partial differential equation (SPDE) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force. Here the extra stress tensor of the fluid is given by a polynomial…

The well-posedness is established for McKean-Vlasov SDEs driven by $\alpha$-stable noises ($1<\alpha<2$). In this model, the drift is H\"{o}lder continuous in space variable and Lipschitz continuous in distribution variable with respect to…

We give an example of a reflected diffferential equation which may have infinitely many solutions if the driving signal is rough enough (e.g. of infinite $p$-variation, for some $p>2$). For this equation, we identify a sharp condition on…

A linear stochastic vector advection equation is considered. The equation may model a passive magnetic field in a random fluid. The driving velocity field is a integrable to a certain power and the noise is infinite dimensional. We prove…

We consider two related linear PDE's perturbed by a fractional Brownian motion. We allow the drift to be discontinuous, in which case the corresponding deterministic equation is ill-posed. However, the noise will be shown to have a…

By using Zvonkin's transformation and a two-step fixed point argument in distributions, the well-posedness and regularity estimates are derived for singular McKean-Vlasov SDEs with distribution dependent noise, where the drift contains a…

The one-dimensional motion of any number $\cN$ of particles in the field of many independent waves (with strong spatial correlation) is formulated as a second-order system of stochastic differential equations, driven by two Wiener…

For $\alpha\in (0,1)$, we consider stochastic differential equations driven by one-sided stable processes of order $\alpha$: \[dX_t= \phi(X_{t-})\ dZ_t.\] We prove that pathwise uniqueness holds for this equation under the assumptions that…

We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter $H\in (1/2,1)$, and contains a non--trivial coefficient in…

We investigate existence, uniqueness and regularity for solutions of rough parabolic equations of the form $\partial _tu-A_tu-f=(\dot X_t(x) \cdot \nabla + \dot Y_t(x))u$ on $[0,T]\times\mathbb{R}^d.$ To do so, we introduce a concept of…

In this paper, we prove pathwise uniqueness for stochastic degenerate systems with a H{\"o}lder drift, for a H{\"o}lder exponent larger than the critical value 2/3. This work extends to the degenerate setting the earlier results obtained by…

We generalize Lyons' rough paths theory in order to give a pathwise meaning to some nonlinear infinite-dimensional evolution equation associated to an analytic semigroup and driven by an irregular noise. As an illustration, we discuss a…

We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [16]. We provide several criteria for existence and uniqueness of…

In this article, a class of second order differential equations on [0,1], driven by a general H\"older continuous function and with multiplicative noise, is considered. We first show how to solve this equation in a pathwise manner, thanks…

In this paper, we prove local existence and uniqueness of analytic sharp-front solutions to a generalised SQG equation by the use of an abstract Cauchy--Kowalevskaya theorem. Here, the velocity is determined by $u =…

We introduce a weak solution concept (called "rough weak solutions") for singular SDEs with additive alpha-stable L\'evy noise (including the Brownian noise case) and prove its equivalence to martingale solutions from Kremp, Perkowski '22…

We study the existence and uniqueness, the regularity, and the long-time behavior of strong solutions to stochastic curve shortening flow driven by a transport-type pure jump L\'evy noise. To obtain the existence and uniqueness of strong…

We prove pathwise (hence strong) uniqueness of solutions to stochastic evolution equations in Hilbert spaces with merely measurable bounded drift and cylindrical Wiener noise, thus generalizing Veretennikov's fundamental result on…

Based on a class of moderately interacting particle systems, we establish a quantitative approximation for density-dependent McKean-Vlasov SDEs and the corresponding nonlinear, nonlocal PDEs. The SDE is driven by both Brownian motion and…