Related papers: Nonlinear Feynman-Kac formulae for SPDEs with spac…
The main goal of this article is to study the effect of small, highly nonlinear, unbounded drifts (small time large deviation principle (LDP) based on exponential equivalence arguments) for a class of stochastic partial differential…
The Feynman-Kac equation governs the distribution of the statistical observable -- functional, having wide applications in almost all disciplines. After overcoming challenges from the time-space coupled nonlocal operator and the possible…
Motivated by applications to a manifold of semilinear and quasilinear stochastic partial differential equations (SPDEs) we establish the existence and uniqueness of strong solutions to coercive and locally monotone SPDEs driven by L\'{e}vy…
We consider the numerical approximation of a general second order semi--linear parabolic stochastic partial differential equation (SPDEs) driven by space-time noise, for multiplicative and additive noise. We examine convergence of…
We consider singular quasilinear stochastic partial differential equations (SPDEs) studied in \cite{FHSX}, which are defined in paracontrolled sense. The main aim of the present article is to establish the global-in-time solvability for a…
The Bismut formula is a crucial tool characterizing regularities of stochastic systems, and has been extensively studied for various models. However it is not yet available for SDEs with distribution dependent noise. In this paper, we first…
In this paper we present two numerical schemes of approximating solutions of backward doubly stochastic differential equations (BDSDEs for short). We give a method to discretize a BDSDE. And we also give the proof of the convergence of…
Existence, uniqueness and non-explosion of the mild solution are proved for a class of semi-linear functional SPDEs with multiplicative noise and Dini continuous drifts. In the finite-dimensional and bounded time delay setting, the…
We prove an existence and uniqueness result for two-obstacle problem for quasilinear Stochastic PDEs (DOSPDEs for short). The method is based on the probabilistic interpretation of the solution by using the backward doubly stochastic…
In this paper, we study the existence of random periodic solutions for semilinear stochastic differential equations. We identify them as solutions of coupled forward-backward infinite horizon stochastic integral equations (IHSIEs), using…
Stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains driven by a multiplicative Gaussian noise are considered. The noise term depends on the unknown velocity and its spatial derivatives. The existence of a martingale…
Marcus stochastic differential equations (SDEs) often are appropriate models for stochastic dynamical systems driven by non-Gaussian Levy processes and have wide applications in engineering and physical sciences. The probability density of…
In this paper, we study the stochastic partial differential equation with multiplicative noise $\frac{\partial u}{\partial t} =\mathcal L u+u\dot W$, where $\mathcal L$ is the generator of a symmetric L\'evy process $X$ and $\dot W$ is a…
The BMO martingale theory is extensively used to study nonlinear multi-dimensional stochastic equations (SEs) in $\cR^p$ ($p\in [1, \infty)$) and backward stochastic differential equations (BSDEs) in $\cR^p\times \cH^p$ ($p\in (1, \infty)$)…
We study the spatial homogenisation of parabolic linear stochastic PDEs exhibiting a two-scale structure both at the level of the linear operator and at the level of the Gaussian driving noise. We show that in some cases, in particular when…
This paper presents theoretical advances in the application of the Stochastic Partial Differential Equation (SPDE) approach in geostatistics. We show a general approach to construct stationary models related to a wide class of linear SPDEs,…
In this paper we propose and analyze explicit space-time discrete numerical approximations for additive space-time white noise driven stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities such as the…
We consider stochastic partial differential equations on $\mathbb{R}^{d}, d\geq 1$, driven by a Gaussian noise white in time and colored in space, for which the pathwise uniqueness holds. By using the Skorokhod representation theorem we…
In this paper we investigate classical solution of a semi-linear system of backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. By proving an It\^{o}-Wentzell formula for jump…
In this paper we study a class of backward stochastic differential equations (BSDEs) of the form dY(t)= -AY(t)dt -f_0(t,Y(t))dt -f_1(t,Y(t),Z(t))dt + Z(t)dW(t) on the interval [0,T], with given final condition at time T, in an infinite…