Existence and uniqueness theorems are given for RODEs under classical and Carathéodory
assumptions. In the latter case the measurability of solutions is also established. Conditions …

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 stack of iterated integrals of a path is embedded in a larger algebraic structure where
iterated integrals are indexed by decorated rooted trees and where an extended Chen's …

The numerical solution of stochastic partial differential equations (SPDEs) is at a stage of
development roughly similar to that of stochastic ordinary differential equations (SODEs) in …

A new class of stochastic Runge–Kutta methods for the weak approximation of the solution
of Itô stochastic differential equation systems with a multidimensional Wiener process is …

The solution of a parabolic stochastic partial differential equation (SPDE) driven by an
infinite-dimensional Brownian motion is in general not a semi-martingale anymore and does …

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 …

A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation
systems wrt a one-dimensional Wiener process is introduced. The colored rooted tree …

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 …

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 …