Related papers: Convergent finite difference schemes for stochasti…
We study a second order BDF (Backward Differentiation Formula) scheme for the numerical approximation of parabolic HJB (Hamilton-Jacobi-Bellman) equations. The scheme under consideration is implicit, non-monotone, and second order accurate…
We introduce a convergent finite difference method for solving the optimal transportation problem on the sphere. The method applies to both the traditional squared geodesic cost (arising in mesh generation) and a logarithmic cost (arising…
We propose a new explicit numerical scheme for stochastic differential equation with super-linearly growing drift and linearly growing diffusion coefficients which are also twice continuously differentiable. The rate of strong convergence…
In this paper we consider multi-dimensional partial differential equations of parabolic type involving divergence form operators that possess a discontinuous coefficient matrix along some smooth interface. The solution of the equation is…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
Stochastic difference equations and a stochastic partial differential equation (SPDE) are simultaneously derived for the time-dependent neutron angular density in a general three-dimensional medium where the neutron angular density is a…
A probabilistic approach for estimating sample qualities for stochastic differential equations is introduced in this paper. The aim is to provide a quantitative upper bound of the distance between the invariant probability measure of a…
This paper is concerned with monotone (time-explicit) finite difference schemes associated with first order Hamilton-Jacobi equations posed on a junction. They extend the schemes recently introduced by Costeseque, Lebacque and Monneau…
In process operations, it is desirable to manage the sensitivity of the system output against external disturbance in the form of finite $\mathcal{L}_2$-gain stabilization. This matter is, however, nonsensical for stochastic systems because…
This paper develops necessary and sufficient conditions for the preservation of asymptotic convergence rates of deterministically and stochastically perturbed ordinary differential equations with regularly varying nonlinearity close to…
By using the It\^{o}-Tanaka trick, we prove the unique strong solvability as well as the gradient estimates for stochastic differential equations with irregular drifts in low regularity Lebesgue-H\"{o}lder space $L^q(0,T;{\mathcal…
Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation.…
We consider non-parametric Bayesian estimation of the drift coefficient of a one-dimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions that are…
In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid…
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. Our main interest is on such SPDEs where the…
This paper examines convergence and stability of the two classes of theta-Milstein schemes for stochastic differential equations (SDEs) with non-global Lipschitz continuous coefficients: the split-step theta-Milstein (SSTM) scheme and the…
We discuss the solution of regular and singular Sturm-Liouville problems by means of High Order Finite Difference Schemes. We describe a code to define a discrete problem and its numerical solution by means of linear algebra techniques.…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
In this paper, we analyze a semi-discrete finite difference scheme for a conservation laws driven by a homogeneous multiplicative Levy noise. Thanks to BV estimates, we show a compact sequence of approximate solutions, generated by the…
This paper is concerned with the numerical approximation of stochastic mechanical systems with nonlinear holonomic constraints. Such systems are described by second order stochastic differential-algebraic equations involving an implicitly…