The numerical approximation of stochastic partial differential equations (SPDEs),
specifically, stochastic evolution equations of the parabolic or hyperbolic type, encounters all …

A new class of third order Runge-Kutta methods for stochastic differential equations with
additive noise is introduced. In contrast to Platen's method, which to the knowledge of the …

In this paper stochastic partitioned Runge–Kutta (SPRK) methods are considered. A general
order theory for SPRK methods based on stochastic B-series and multicolored, multishaped …

In this article, we construct a representation formula for stochastic B-series evaluated in a B-
series. This formula is used to give for the first time the order conditions of implicit Taylor …

We discuss stochastic differential equations with a stiff linear part and their approximation by
stochastic exponential Runge–Kutta integrators. Representing the exact and approximate …

For stochastic implicit Taylor methods that use an iterative scheme to compute their
numerical solution, stochastic B-series and corresponding growth functions are constructed …

In thisdissertation, wedealwiththeproblemofsimulatingstochasti… driven
byBrownianmotionorthegeneralL´ evy processes. First, weestablishthebasic theory …

In the last years, implicit SRK methods have been developed both for strong and weak
approximation. For these methods, the stage values are only given implicitly. However, in …