Related papers: Weak order in averaging principle for stochastic w…

We consider a solution $u(\cdot,t)$ to an initial boundary value problem for time-fractional diffusion-wave equation with the order $\alpha \in (0,2) \setminus \{ 1\}$ where $t$ is a time variable. We first prove that a suitable norm of…

This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating slab (between two parallel planes) in the weak-scattering regime, and the study of boundary effects through an…

We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck…

Semiclassical (stochastic) wave equations are proposed for the coupled dynamics of atomic quantum states and semiclassical radiation field. All relevant predictions of standard unitary quantum dynamics are exactly reproducible in the…

This work considers the variable-exponent fractional diffusion-wave equation, which describes, e.g. the propagation of mechanical diffusive waves in viscoelastic media with varying material properties. Rigorous numerical analysis for this…

Let $W$ denote the Brownian motion. For any exponentially bounded Borel function $g$ the function $u$ defined by $u(t,x)= \mathbb{E}[g(x{+}\sigma W_{T-t})]$ is the stochastic solution of the backward heat equation with terminal condition…

Weak convergence of the stochastic evolutionary system to the average evolutionary system is proved. The method proposed by R.Liptser in for semimartingales is used. But we apply a solution of singular perturbation problem instead of…

The classical fluctuation-dissipation theorem predicts the average response of a dynamical system to an external deterministic perturbation via time-lagged statistical correlation functions of the corresponding unperturbed system. In this…

It has been experimentally observed that weakly conducting suspended films of smectic liquid crystals undergo electroconvection when subjected to a large enough potential difference. The resulting counter-rotating vortices form a very…

This paper is concerned with the numerical analysis of the explicit upwind finite volume scheme for numerically solving continuity equations. We are interested in the case where the advecting velocity field has spatial Sobolev regularity…

We study the weak approximation error of a skew diffusion with bounded measurable drift and H\"older diffusion coefficient by an Euler-type scheme, which consists of iteratively simulating skew Brownian motions with constant drift. We first…

In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…

This work is concerned with model reduction of stochastic differential equations and builds on the idea of replacing drift and noise coefficients of preselected relevant, e.g. slow variables by their conditional expectations. We extend…

The time evolution of the two-time conditional probability of the classical stochastic process is described in an analogous form of the quantum mechanical wave equations. By using it, we emulate the same strange behaviors as those of the…

The first article in a two-part series (the second article being [arXiv:2205.13197]) assumes a weak local energy decay estimate holds and proves that solutions to the linear wave equation with variable coefficients in $\mathbb R^{1+3}$,…

Strong convergence rates for time-discrete numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood in the literature. Weak convergence rates for time-discrete…

We establish a novel convergent iteration framework for a weak approximation of general switching diffusion. The key theoretical basis of the proposed approach is a restriction of the maximum number of switching so as to untangle and…

The regularity of solutions to the stochastic nonlinear wave equation plays a critical role in the accuracy and efficiency of numerical algorithms. Rough or discontinuous initial conditions pose significant challenges, often leading to a…

In this paper, we investigate the energy decay of the solution to a viscoelastic wave equation with variable exponents logarithmic nonlinearity and weak damping in a bounded domain. We establish an explicit general decay result under mild…

We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Milstein's weak error analysis on the one-step approximation of…