Related papers: A Wong-Zakai theorem for SDEs with singular drift

Stochastic differential equations are ubiquitous modelling tools in physics and the sciences. In most modelling scenarios, random fluctuations driving dynamics or motion have some non-trivial temporal correlation structure, which renders…

We study the numerical approximation of SDEs with singular drifts (including distributions) driven by a fractional Brownian motion. Under the Catellier-Gubinelli condition that imposes the regularity of the drift to be strictly greater than…

The asymptotic analysis of a class of stochastic partial differential equations (SPDEs) with fully locally monotone coefficients covering a large variety of physical systems, a wide class of quasilinear SPDEs and a good number of fluid…

This paper studies the numerical methods to approximate the solutions for a sort of McKean-Vlasov neutral stochastic differential delay equations (MV-NSDDEs) that the growth of the drift coefficients is super-linear. First, We obtain that…

We generalize the theory of periodic homogenization for multidimensional SDEs with additive Brownian and stable L\'evy noise for $\alpha\in (1,2)$ to the setting of singular periodic Besov drifts of regularity $\beta\in ((2-2\alpha)/3,0)$…

In this article, we construct weak solutions for a class of Stochastic PDEs in the space of tempered distributions via Girsanov's theorem. It is to be noted that our drift and diffusion coefficients $(L,A)$ of the considered Stochastic PDE…

The classical result by It\^o on the existence of strong solutions of stochastic differential equations (SDEs) with Lipschitz coefficients can be extended to the case where the drift is only measurable and bounded. These generalizations are…

We study the ergodic behaviour of the McKean-Vlasov equations driven by common, divergence-free transport noise. In particular, we show that in dimension $d\geq 2$, if the noise is mixing and sufficiently strong it can enforce the…

We study existence and uniqueness of a variational solution in terms of stochastic variational inequalities (SVI) to stochastic nonlinear diffusion equations with a highly singular diffusivity term and multiplicative Stratonovich…

We present a comprehensive discretization scheme for linear and nonlinear stochastic differential equations (SDEs) driven by either Brownian motions or $\alpha$-stable processes. Our approach utilizes compound Poisson particle…

We develop a unified PDE-probabilistic framework for pointwise gradient and Hessian estimates of Markov semigroups associated with stochastic differential equations with singular and unbounded coefficients. Under mild local structural…

In this paper, we prove pathwise uniqueness for stochastic systems of McKean-Vlasov type with singular drift, even in the measure argument, and uniformly non-degenerate Lipschitz diffusion matrix. Our proof is based on Zvonkin's…

We prove global well-posedness for a class of dissipative semilinear stochastic evolution equations with singular drift and multiplicative Wiener noise. In particular, the nonlinear term in the drift is the superposition operator associated…

The solutions of SDEs with multiplicative noise are not Markovian. On a coarse-grained time scale they still are, but only in the "anti-Ito" case. This allows a simple computation of the most likely path. Any density peak moves along such a…

In this paper we study solutions to stochastic differential equations (SDEs) with discontinuous drift. We apply two approaches: The Euler-Maruyama method and the Fokker-Planck equation and show that a candidate density function based on the…

We establish the existence and uniqueness of strong solutions, in both the PDE and probabilistic sense, for a broad class of nonlinear stochastic partial differential equations (SPDEs) on a bounded domain $\mathscr{O}\subset \mathbb{R}^d$…

We study strong approximation of scalar additive noise driven stochastic differential equations (SDEs) at time point $1$ in the case that the drift coefficient is bounded and has Sobolev regularity $s\in(0,1)$. Recently, it has been shown…

In this work, we establish the existence and uniqueness of solutions to McKean-Vlasov stochastic differential equations (SDEs) driven by L\'evy processes with common noise on an infinite time horizon, by means of a contraction mapping…

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…

We study stochastic parabolic and elliptic PDEs driven by purely spatial white noise. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. We…