Related papers: Counterexamples to local Lipschitz and local H\"ol…

In this paper, we establish a large deviation principle for a type of stochastic partial differential equations (SPDEs) with locally monotone coefficients driven by L\'evy noise. The weak convergence method plays an important role.

We prove existence and uniqueness of mild and generalized solutions for a class of stochastic semilinear evolution equations driven by additive Wiener and Poisson noise. The non-linear drift term is supposed to be the evaluation operator…

It is well known that for a stochastic differential equation driven by L\'evy noise, the temporal H\"older continuity in $L^p$ sense of the exact solution does not exceed $1/p$. This leads to that the $L^p$-strong convergence order of a…

We consider a one-dimensional stochastic differential equations (SDE) with irregular coefficients. The purpose of this paper is to estimate the $L^p(\Omega)$-difference of SDEs using the norm of the difference of coefficients, where the…

We obtain sufficient condition for SDEs to evolve in the positive orthant. We use comparison theorem arguments to achieve this. As a result we prove the existence of a unique strong solution for a class of multidimensional degenerate SDEs…

We establish two-sided weighted integrability estimates, often referred to as a norm equivalence result, for stochastic differential equations (SDEs) with locally Lipschitz coefficients. As a key ingredient in our approach, we also derive…

This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise under more relaxed conditions. The SPDE is discretized…

The Bismut formula is established for the intrinsic derivative of singular McKean-Vlasov SDEs, where the noise coefficient belongs to a local Sobolev space, and the drift contains a locally integrable time-space term as well as a…

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 study parameter estimation for univariate stochastic differential equations with locally Lipschitz drift and H\"older continuous multiplicative diffusion, a class commonly arising in several applications. Existing inference methods…

We devise an explicit method to integrate $\alpha$-stable stochastic differential equations (SDEs) with non-Lipschitz coefficients. To mitigate against numerical instabilities caused by unbounded increments of the L\'evy noise, we use a…

Existence, uniqueness, and regularity of a strong solution are obtained for stochastic PDEs with a colored noise $F$ and its super-linear diffusion coefficient: $$ du=(a^{ij}u_{x^ix^j}+b^iu_{x^i}+cu)dt+\xi|u|^{1+\lambda}dF, \quad…

In recent years, interest in approximation methods for stochastic differential equations (SDEs) with non-Lipschitz continuous coefficients has increased. We show lower bounds for the $L^p$-error of such methods in the case of approximation…

We show that that the stochastic 3D primitive equations with either the physical boundary conditions or Neumann boundary conditions on the top and bottom and Dirichlet boundary condition on the sides driven by multiplicative…

We consider a class of generalised stochastic porous media equations with multiplicative Lipschitz continuous noise. These equations can be related to physical models exhibiting self-organised criticality. We show that these SPDEs have…

This paper introduces a class of backward stochastic differential equations (BSDEs), whose coefficients not only depend on the value of its solutions of the present but also the past and the future. For a sufficiently small time delay or a…

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…

In this article, we consider a stochastic partial differential equation (SPDE) driven by a L\'evy white noise, with Lipschitz multiplicative term $\sigma$. We prove that under some conditions, this equation has a unique random field…

In this paper we prove several results related to the existence and uniqueness of solution to coupled highly nonlinear stochastic partial differential equations (PDEs). These equations are motivated by the dynamics of nematic liquid…

The celebrated H\"{o}rmander condition is a sufficient (and nearly necessary) condition for a second-order linear Kolmogorov partial differential equation (PDE) with smooth coefficients to be hypoelliptic. As a consequence, the solutions of…