Related papers: Semilinear stochastic partial differential equatio…

Machine learning of partial differential equations from data is a potential breakthrough to solve the lack of physical equations in complex dynamic systems, but because numerical differentiation is ill-posed to noise data, noise has become…

We consider statistics for stochastic evolution equations in Hilbert space with emphasis on stochastic partial differential equations (SPDEs). We observe a solution process under additional measurement errors and want to estimate a real or…

The convective Brinkman-Forchheimer (CBF) equations characterize the motion of incompressible fluid flows in a saturated porous medium. The small noise asymptotic for the two-time-scale stochastic convective Brinkman-Forchheimer (SCBF)…

For a L\'evy basis $L$ on $\mathbb{R}^d$ and a suitable kernel function $f:\mathbb{R}^d \to \mathbb{R}$, consider the continuous spatial moving average field $X=(X_t)_{t\in \mathbb{R}^d}$ defined by $X_t = \int_{\mathbb{R}^d} f(t-s) \,…

These notes are based on a series of lectures given first at the University of Warwick in spring 2008 and then at the Courant Institute, Imperial College London, and EPFL. It is an attempt to give a reasonably self-contained presentation of…

This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise,…

We consider the control of semilinear stochastic partial differential equations (SPDEs) via deterministic controls. In the case of multiplicative noise, existence of optimal controls and necessary conditions for optimality are derived. In…

This paper provides a comprehensive Sobolev regularity theory for the Dirichlet problem of stochastic partial differential equations in $C^{1,\sigma}$ open sets. We consider substantially large classes of nonlocal operators and generalized…

We investigate a class of stochastic partial differential equations of reaction-diffusion type defined on graphs, which can be derived as the limit of SPDEs on narrow planar channels. In the first part, we demonstrate that this limit can be…

This is basically a polished presentation for Sections 1,2 of arXiv:0801.1050. The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and…

We establish a general criterion which ensures exponential mixing of parabolic Stochastic Partial Differential Equations (SPDE) driven by a non additive noise which is white in time and smooth in space. We apply this criterion on two…

We propose and analyse a boundary-preserving numerical scheme for the weak approximation for some stochastic partial differential equations (SPDEs) with bounded state-space. We impose regularity assumptions on the drift and diffusion…

The large deviation principle is established for the distributions of a class of generalized stochastic porous media equations for both small noise and short time.

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson…

The present work deals with the global solvability as well as asymptotic analysis of stochastic generalized Burgers-Huxley (SGBH) equation perturbed by space-time white noise in a bounded interval of $\mathbb{R}$. We first prove the…

This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions. It is shown…

We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…

Dynamical system models with delayed dynamics and small noise arise in a variety of applications in science and engineering. In many applications, stable equilibrium or periodic behavior is critical to a well functioning system. Sufficient…

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…

We consider a system of semi-linear partial differential equations with measurable coefficients and a nonlinear Neumann boundary condition. We then construct a sequence of penalized partial differential equations which converges to a…