Related papers: Form-boundedness and SDEs with singular drift
For a mixed stochastic differential equation involving standard Brownian motion and an almost surely H\"older continuous process $Z$ with H\"older exponent $\gamma>1/2$, we establish a new result on its unique solvability. We also establish…
In this paper we investigate two variants of $\alpha$-stable processes, namely tempered stable subordinators and modified tempered stable process as well as their renormalization. We study the weak convergence in the Skorohod space and…
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 paper, we study (strong and weak) existence and uniqueness of a class of non-Markovian SDEs whose drift contains the derivative in the sense of distributionsof a continuous function.
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such…
In this paper, we show that the minimal solution of a backward stochastic differential equation gives a probabilistic representation of the minimal viscosity solution of an integro-partial differential equation both with a singular terminal…
In this paper we shall establish an existence and uniqueness result for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst…
We show the existence and uniqueness as well as boundedness of weak solutions to linear elliptic equations with $L^2$-drifts of negative divergence and singular zero-order terms which are positive. Our main target is to show the…
We concern the effect of domain perturbation on the behaviour of stochastic partial differential equations subject to the Dirichlet boundary condition. Under some assumptions, we get an estimate for the solutions under changes of the…
We put forward a new method for proving weak uniqueness of stochastic equations with singular drifts driven by a non-Markov or infinite-dimensional noise. We apply our method to study stochastic heat equation (SHE) driven by Gaussian…
We obtain the unique weak and strong solvability for time inhomogeneous stochastic differential equations with the drift in subcritical Lebesgue--H\"{o}lder spaces $L^p([0,T];{\mathcal C}_b^{\beta}({\mathbb R}^d;{\mathbb R}^d))$ and driven…
Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
We show the strong well-posedness of SDEs driven by general multiplicative L\'evy noises with Sobolev diffusion and jump coefficients and integrable drift. Moreover, we also study the strong Feller property, irreducibility as well as the…
In this work we mainly prove the existence and pathwise uniqueness of solutions to general backward doubly stochastic differential equations with jumps appearing in both forward and backward integral parts. Several comparison theorems under…
We prove an existence and uniqueness result for quasilinear Stochastic PDEs with Obstacle (in short OSPDE) under a weaker integrability condition on the coefficient and the barrier.
In this paper we study jump-diffusion stochastic differential equations (SDEs) with a discontinuous drift coefficient and a possibly degenerate diffusion coefficient. Such SDEs appear in applications such as optimal control problems in…
We provide a general framework for the stability of solutions to stochastic partial differential equations with respect to perturbations of the drift. More precisely, we consider stochastic partial differential equations with drift given as…
This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…