相关论文: A note on Asymptotic mean-square stability of stoc…

In this article we investigate consistency and asymptotic normality of the maximum likelihood and the posterior distribution of the parameters in the context of state space stochastic differential equations (SDEs). We then extend our…

In this paper, we initiate the study of backward doubly stochastic differential equations (BDSDEs, for short) with quadratic growth. The existence, comparison, and stability results for one-dimensional BDSDEs are proved when the generator…

We develop a method to prove almost global stability of stochastic differential equations in the sense that almost every initial point (with respect to the Lebesgue measure) is asymptotically attracted to the origin with unit probability.…

Linear multistep methods (LMMs) applied to approximate the solution of initial value problems---typically arising from method-of-lines semidiscretizations of partial differential equations---are often required to have certain monotonicity…

In this paper, we analyze the asymptotic properties of the Two-Stage (TS) estimator -- a simulation-based parameter estimation method that constructs estimators offline from synthetic data. While TS offers significant computational…

High order strong stability preserving (SSP) time discretizations are often needed to ensure the nonlinear (and sometimes non-inner-product) strong stability properties of spatial discretizations specially designed for the solution of…

We demonstrate how to produce a stable multispeed lattice Boltzmann method (LBM) for a wide range of velocity sets, many of which were previously thought to be intrinsically unstable. We use non-Gauss--Hermitian cubatures. The method…

The companion paper "Higher-order in time quasi-unconditionally stable ADI solvers for the compressible Navier-Stokes equations in 2D and 3D curvilinear domains", which is referred to as Part I in what follows, introduces ADI (Alternating…

In this article we investigate the numerical solution of a scalar semilinear stochastic delay differential equation (SDDE) where the linear instantaneous feedback and nonlinear delayed feedback terms are perturbed by a pair of standard…

The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In…

We present an asymptotic preserving scheme based on a micro-macro decomposition for stochastic linear transport equations in kinetic and diffusive regimes. We perfom a mathematical analysis and prove that the scheme is uniformly stable with…

This paper is concerned with the numerical approximation of stochastic ordinary differential equations, which satisfy a global monotonicity condition. This condition includes several equations with super-linearly growing drift and diffusion…

Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…

In this paper, we investigate the asymptotic stability threshold problem for the 2-D Navier-Stokes equations in a finite channel with no-slip boundary conditions, around monotone shear flow $(U(t,y),0)$. We establish that the flow is…

Delattre et al. (2013) considered a system of stochastic differential equations (SDEs) in a random effects setup. Under the independent and identical (iid) situation, and assuming normal distribution of the random effects, they established…

Under non-global Lipschitz condition, Euler Explicit method fails to converge strongly to the exact solution, while Euler implicit method converges but requires much computational efforts. Tamed scheme was first introduced in [2] to…

The recently developed technique of DOC kernels has been a great success in the stability and convergence analysis for BDF2 scheme with variable time steps. However, such an analysis technique seems not directly applicable to problems with…

Numerical analysis for linear constant-coefficients Finite Difference schemes was developed approximately fifty years ago. It relies on the assumption of scheme stability and in particular -- for the $L^2$ setting -- on the absence of…

Previous studies on two-timescale stochastic approximation (SA) mainly focused on bounding mean-squared errors under diminishing stepsize schemes. In this work, we investigate {\it constant} stpesize schemes through the lens of Markov…

This paper investigates the long time stability behavior of multiphysics flow problems, namely the Navier-Stokes equations, natural convection and double-diffusive convection equations with an extrapolated blended BDF time-stepping scheme.…