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 …

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 introduce a new algebraic framework based on a modification (called exotic) of aromatic
Butcher-series for the systematic study of the accuracy of numerical integrators for the …

The aim of the work presented in this thesis is the construction and the study of numerical
integrators in time to solve stochastic differential equations (SDEs) and stochastic partial …

In this paper a set of previous general results for the development of B--series for a broad
class of stochastic differential equations has been collected. The applicability of these …

We show that applying any deterministic B-series method of order pd with a random step
size to single integrand SDEs gives a numerical method converging in the mean-square and …

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 this paper we introduce a family of stochastic Runge–Kutta Rosenbrock (SRKR) type
methods for multi-dimensional Itô stochastic differential equations (SDEs). The presented …

Exercise 1: Provide the list of trees τ T with a number of nodes| τ|¤ 5 in the set T of trees. For
each of them, calculate the coefficients γpτq and σpτq as defined in the course. Show that …