Related papers: Boundary-preserving weak approximation for some se…
We present an explicit method for simulating stochastic differential equations (SDEs) that have variable diffusion coefficients and satisfy the detailed balance condition with respect to a known equilibrium density. In Tupper and Yang…
We prove a general criterion providing sufficient conditions under which a time-discretiziation of a given Stochastic Differential Equation (SDE) is a uniform in time approximation of the SDE. The criterion is also, to a certain extent,…
We survey recent developments in the field of complexity of pathwise approximation in $p$-th mean of the solution of a stochastic differential equation at the final time based on finitely many evaluations of the driving Brownian motion.…
In this article, we extend a Milstein finite difference scheme introduced in [Giles & Reisinger(2011)] for a certain linear stochastic partial differential equation (SPDE), to semi- and fully implicit timestepping as introduced by…
We study strong approximation of $d$-dimensional stochastic differential equations (SDEs) with a discontinuous drift coefficient. More precisely, we essentially assume that the drift coefficient is piecewise Lipschitz continuous with an…
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…
A new modification of the minimum-contrast estimator (the weighted MCE) of drift parameter in a linear stochastic evolution equation with additive fractional noise is introduced in the setting of the spectral approach (Fourier coordinates…
The present work introduces and investigates an explicit time discretization scheme, called the projected Euler method,to numerically approximate random periodic solutions of semi-linear SDEs under non-globally Lipschitz conditions. The…
We present an abstract concept for the error analysis of numerical schemes for semilinear stochastic partial differential equations (SPDEs) and demonstrate its usefulness by proving the strong convergence of a Milstein-Galerkin finite…
The strong convergence of Euler approximations of stochastic delay differential equations is proved under general conditions. The assumptions on drift and diffusion coefficients have been relaxed to include polynomial growth and only…
We study a family of numerical schemes applied to a class of multiscale systems of stochastic differential equations. When the time scale separation parameter vanishes, a well-known Smoluchowski--Kramers diffusion approximation result…
In this paper, a higher-order time-discretization scheme is proposed, where the iterates approximate the solution of the stochastic semilinear wave equation driven by multiplicative noise with general drift and diffusion. We employ a…
The paper deals with the numerical solution of the nonlinear Ito stochastic differential equations (SDEs) appearing in the unravelling of quantum master equations. We first develop an exponential scheme of weak order 1 for general globally…
We present an implicit Split-Step explicit Euler type Method (dubbed SSM) for the simulation of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts of superlinear growth in space, Lipschitz in measure and non-constant…
This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…
In this paper, we study two kinds of structure-preserving splitting methods, including the Lie--Trotter type splitting method and the finite difference type method, for the stochasticlogarithmic Schr\"odinger equation (SlogS equation) via a…
This paper is devoted to studying the averaging principle for stochastic differential equations with slow and fast time-scales, where the drift coefficients satisfy local Lipschitz conditions with respect to the slow and fast variables, and…
In this paper, we study the numerical approximation of a general second order semilinear stochastic partial differential equation (SPDE) driven by a additive fractional Brownian motion (fBm) with Hurst parameter $H>\frac 12$ and Poisson…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
We introduce a lattice random walk discretisation scheme for stochastic differential equations (SDEs) that samples binary or ternary increments at each step, suppressing complex drift and diffusion computations to simple 1 or 2 bit random…