Some new stochastic Runge–Kutta (SRK) methods for the strong approximation of solutions
of stochastic differential equations (SDEs) with improved efficiency are introduced. Their …

The paper provides a nonlinear stability analysis for a class of stochastic Runge-Kutta
methods, applied to problems generating mean-square contractive solutions. In particular …

While backward error analysis does not generalise straightforwardly to the strong and weak
approximation of stochastic differential equations, it extends for the sampling of ergodic …

We derive a new methodology for the construction of high-order integrators for sampling the
invariant measure of ergodic stochastic differential equations with dynamics constrained on …

Traditional explicit schemes such as the Euler-Maruyama, Milstein and stochastic Runge-
Kutta methods, in general, result in strong and weak divergence when solving stochastic …

This study concerns the approximation of some stochastic integrals used in the strong
second-order methods for several classes of stochastic differential equations. An explicit …

The paper is focused on analyzing the linear stability properties of stochastic Runge–Kutta
(SRK) methods interpreted as a stochastic perturbation of the corresponding deterministic …

B-Series and generalizations are a powerful tool for the analysis of numerical integrators. An
extension named exotic aromatic B-Series was introduced to study the order conditions for …

We present an error analysis of weak convergence of one-step numerical schemes for
stochastic differential equations (SDEs) with super-linearly growing coefficients. Following …

In this paper, all the terms in the stochastic Magnus expansion are presented by rooted
trees. First, stochastic Magnus methods for linear stochastic differential equations are …