相关论文: Pathwise Uniqueness for SDEs with Singular Drift a…

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…

In this article we prove the pathwise uniqueness for stochastic differential equations in $\mR^d$ with time-dependent Sobolev drifts, and driven by symmetric $\alpha$-stable processes provided that $\alpha\in(1,2)$ and its spectral measure…

We study well-posedness for the stochastic transport equation with transport noise, as introduced by Flandoli, Gubinelli and Priola. We consider periodic solutions in $\rho \in L^{\infty}_{t} L_{x}^{p}$ for divergence-free drifts $u \in…

Under integrability conditions on distribution dependent coefficients, existence and uniqueness are proved for McKean-Vlasov type SDEs with non-degenerate noise. When the coefficients are Dini continuous in the space variable, gradient…

In our previous paper [Ekren, Touzi and Zhang (2015)], we introduced a notion of viscosity solutions for fully nonlinear path-dependent PDEs, extending the semilinear case of Ekren et al. [Ann. Probab. 42 (2014) 204-236], which satisfies a…

A new strong uniqueness result for a multidimensional SDE with a non-degenerate diffusion and partially irregular drift is established. It may be regarded as a combined variation on the themes of Yamada \& Watanabe (1971), of Zvonkin…

In this paper linear stochastic transport and continuity equations with drift in critical $L^{p}$ spaces are considered. In this situation noise prevents shocks for the transport equation and singularities in the density for the continuity…

Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE…

We study stochastic differential equations(SDEs) with a small perturbation parameter. Under the dissipative condition on the drift coefficient and the local Lipschitz condition on the drift and diffusion coefficients we prove the existence…

In this paper, we prove a uniqueness result in the inverse problem of determining several non-constant coefficients of one-dimensional reaction-diffusion equations. Such reaction-diffusion equations include the classical model of…

In this paper we introduce a transformation technique, which can on the one hand be used to prove existence and uniqueness for a class of SDEs with discontinuous drift coefficient. One the other hand we present a numerical method based on…

We prove pathwise nonuniqueness in the stochastic partial differential equations (SPDEs) for some one-dimensional super-Brownian motions with immigration. In contrast to a closely related case investigated by Mueller, Mytnik and Perkins…

Local diffusion of strictly hyperbolic higher-order PDE's with constant coefficients at all simple singularities of corresponding wavefronts can be explained and recognized by only two local geometrical features of these wavefronts. We…

We prove strong well-posedness for a class of stochastic evolution equations in Hilbert spaces H when the drift term is Holder continuous. This class includes examples of semilinear stochastic damped wave equations which describe elastic…

We establish a novel uniqueness result for an instationary drift-diffusion model for perovskite solar cells. This model for vacancy-assisted charge transport uses Fermi--Dirac statistics for electrons and holes and Blakemore statistics for…

In this paper, we establish the existence of a stochastic flow of Sobolev diffeomorphisms \[\mathbb{R}^d\ni x\quad\longmapsto\quad\phi_{s,t}(x)\in \mathbb{R}^d,\qquad s,t\in\mathbb{R}\] for a stochastic differential equation (SDE) of the…

We study the long-time behaviour of solutions to a class of $d$-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H \in (0,1)$. The drift consists of a dissipative Lipschitz term and a…

In a previous work [8], it was shown that the joint law of a diffusion process and the running supremum of its first component is absolutely continuous, and that its density satisfies a non standard weak partial differential equation (PDE).…

We consider a process given as the solution of a stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. Explicit and optimal bounds for the Lebesgue density of that…

This paper is devoted to existence and uniqueness results for classes of nonlinear diffusion equations (or systems) which may be viewed as regular perturbations of Wasserstein gradient flows. First, in the case. where the drift is a…