相关论文: Weak error analysis for strong approximation schem…

This paper develops methods for numerically solving stochastic delay-differential equations (SDDEs) with multiple fixed delays that do not align with a uniform time mesh. We focus on numerical schemes of strong convergence orders $1/2$ and…

In this paper, we consider the numerical approximation of a general second order semilinear stochastic partial differential equation (SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the nonlinear…

This article investigates the weak approximation towards the invariant measure of semi-linear stochastic differential equations (SDEs) under non-globally Lipschitz coefficients. For this purpose, we propose a linear-theta-projected Euler…

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…

For semilinear stochastic evolution equations whose coefficients are more general than the classical global Lipschitz, we present results on the strong convergence rates of numerical discretizations. The proof of them provides a new…

We propose a geometric numerical analysis of SDEs admitting Lie symmetries which allows us to individuate a symmetry adapted coordinates system where the given SDE has notable invariant properties. An approximation scheme preserving the…

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…

In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are…

In this paper, we first establish well-posedness of McKean-Vlasov stochastic differential equations (McKean-Vlasov SDEs) with common noise, possibly with coefficients having super-linear growth in the state variable. Second, we present…

We review, implement, and compare numerical integration schemes for spatially bounded diffusions stopped at the boundary which possess a convergence rate of the discretization error with respect to the timestep $h$ higher than ${\cal…

This work introduces a general framework for establishing the long time accuracy for approximations of Markovian dynamical systems on separable Banach spaces. Our results illuminate the role that a certain uniformity in Wasserstein…

This paper develops a framework for the error analysis in nonparametric model fitting of fractional stochastic differential equations based on discrete observations. We identify and quantify the main error sources -- time discretization,…

The problem of approximating the covariance operator of the mild solution to a linear stochastic partial differential equation is considered. An integral equation involving the semigroup of the mild solution is derived and a general error…

The numerical approximation of the solution to a stochastic partial differential equation with additive spatial white noise on a bounded domain is considered. The differential operator is assumed to be a fractional power of an integer order…

We introduce an explicit, adaptive time-stepping scheme for the simulation of SPDEs with one-sided Lipschitz drift coefficients. Strong convergence rates are proven for the full space-time discretisation with multiplicative trace-class…

This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…

Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…

We give a new take on the error analysis of approximations of stochastic differential equations (SDEs), utilizing and developing the stochastic sewing lemma of L\^e (2020). This approach allows one to exploit regularization by noise effects…

We propose and study a scheme combining the finite element method and machine learning techniques for the numerical approximations of coupled nonlinear forward-backward stochastic partial differential equations (FBSPDEs) with homogeneous…

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…