Related papers: Stochastic It\^o Equations and Parabolic Second-Or…

For time-homogeneous stochastic differential equations (SDEs) it is enough to know that the coefficients are Lipschitz to conclude existence and uniqueness of a solution, as well as the existence of a strongly convergent numerical method…

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…

We investigate uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of fractional parabolic and elliptic equations with a drift.

We prove pathwise uniqueness for a class of stochastic differential equations (SDE) on a Hilbert space with cylindrical Wiener noise, whose nonlinear drift parts are sums of the sub-differential of a convex function and a bounded part. This…

We explore Ito stochastic differential equations where the drift term possibly depends on the infinite past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of…

We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…

This paper focuses on recent works on McKean-Vlasov stochastic differential equations (SDEs) involving singular coefficients. After recalling the classical framework, we review existing recent literature depending on the type of…

In this paper, we consider a new approach for semi-discretization in time and spatial discretization of a class of semi-linear stochastic partial differential equations (SPDEs) with multiplicative noise. The drift term of the SPDEs is only…

In this paper we present a new method for the construction of strong solutions of SDE's with merely integrable drift coefficients driven by a multidimensional fractional Brownian motion with Hurst parameter H < 1/2. Furthermore, we prove…

In this paper, we prove weak uniqueness of hypoelliptic stochastic differential equation with H{\"o}lder drift, with H{\"o}lder exponent strictly greater than 1/3. We then extend to a weak framework the previous work [CdR12] where strong…

In this paper, the optimal strong error estimates for stochastic parabolic optimal control problem with additive noise and integral state constraint are derived based on time-implicit and finite element discretization. The continuous and…

In this paper we present a scheme for the numerical solution of one-dimensional stochastic differential equations (SDEs) whose drift belongs to a fractional Sobolev space of negative regularity (a subspace of Schwartz distributions). We…

By using some recent results for divergence form equations, we study the $L_p$-solvability of second-order elliptic and parabolic equations in nondivergence form for any $p\in (1,\infty)$. The leading coefficients are assumed to be in…

We prove existence and uniqueness of solutions to a nonlinear stochastic evolution equation on the $d$-dimensional torus with singular $p$-Laplace-type or total variation flow-type drift with general sublinear doubling nonlinearities and…

We show how the parabolic version of the Adams theorem and its corollary can be used to estimate in $L_{p}$ the evolution family associated to a divergence form second-order parabolic operator with parabolic Morrey lower-order terms and…

In this paper we consider the It\^o SDE $$d X_t=d W_t+b(t,X_t)\,d t, \quad X_0=x\in {\mathbb R}^d,$$ where $W_t$ is a $d$-dimensional standard Wiener process and the drift coefficient $b:[0,T]\times{\mathbb R}^d\to{\mathbb R}^d$ belongs to…

We establish the well-posedness of SDE with the additive noise when a singular drift belongs to the critical spaces. We prove that if the drift belongs to the Orlicz-critical space $L^{q,1}([0,T],L^p_x)$ for $p,q\in (1,\infty)$ satisfying…

In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…

The aim of this paper is to develop a sequence of discrete approximations to a one-dimensional It\^o diffusion that almost surely converges to a weak solution of the given stochastic differential equation. Under suitable conditions, the…

In this paper, we are interested in the following singular stochastic differential equation (SDE) $${\rm d} X_t = b(t,X_t) {\rm d} t + {\rm d} B_{t},\ 0\leq t\leq T,\ X_0 = x \in \mathbb{R}^d,$$ where the drift coefficient $b:[0,T]\times…