相关论文: Time integration of dissipative stochastic PDEs

We study the systematic numerical approximation of Maxwell's equations in dispersive media. Two discretization strategies are considered, one based on a traditional leapfrog time integration method and the other based on convolution…

Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper, we provide…

We extend stochastic basis adaptation and spatial domain decomposition methods to solve time varying stochastic partial differential equations (SPDEs) with a large number of input random parameters. Stochastic basis adaptation allows the…

We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation…

The aim of this review is to provide a concise overview of some of the generic approaches that have been developed to deal with the statistical description of large systems of interacting dissipative 'units'. The latter notion includes,…

This paper studies open-loop equilibriums for a general class of time-inconsistent stochastic control problems under jump-diffusion SDEs with deterministic coefficients. Inspired by the idea of Four-Step-Scheme for forward-backward…

Symmetry methods are by now recognized as one of the main tools to attack deterministic differential equations (both ODEs and PDEs); the situation is quite different for what concerns stochastic differential equations: here, symmetry…

Stability and convergence of a time-weighted discrete scheme with nonuniform time steps are established for linear reaction-subdiffusion equations. The Caupto derivative is approximated at an offset point by using linear and quadratic…

We propose the first $\alpha$-parameterized framework for solving time-changed stochastic differential equations (TCSDEs), explicitly linking convergence rates to the driving parameter of the underlying stochastic processes. Theoretically,…

Time fractional PDEs have been used in many applications for modeling and simulations. Many of these applications are multiscale and contain high contrast variations in the media properties. It requires very small time step size to perform…

The object of this paper is a one-dimensional generalized porous media equation (PDE) with possibly discontinuous coefficient $\beta$, which is well-posed as an evolution problem in $L^1(\mathbb{R})$. In some recent papers of Blanchard et…

In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints is studied. Time discretization is…

We investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic…

This paper addresses the challenge of time-inconsistent stochastic control within a continuous-time framework. Its primary focus lies in uncovering a probabilistic representation, specifically in the shape of a system of backward stochastic…

In this paper, a general theorem on the equivalence of pth moment stability between stochastic differential delay equations (SDDEs) and their numerical methods is proved under the assumptions that the numerical methods are strongly…

We introduce a new approach for designing numerical schemes for stochastic differential equations (SDEs). The approach, which we have called direction and norm decomposition method, proposes to approximate the required solution $X_t$ by…

We introduce a method which provides accurate numerical solutions to fractional-in-time partial differential equations posed on $[0,T] \times \Omega$ with $\Omega \subset \mathbb{R}^d$ without the excessive memory requirements associated…

The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and…

We address the problem of approximating the moments of the solution, $\boldsymbol{X}(t)$, of an It\^o stochastic differential equation (SDE) with drift and a diffusion terms over a time-grid $t_0, t_1, \ldots, t_n$. In particular, we assume…

Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…