This book is a substantially revised and expanded edition reflecting major developments in
stochastic numerics since the 1st edition [314] was published in 2004. The new topics …

On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of
a stochastic differential equation (SDE) with a superlinearly growing and globally one-sided …

Many stochastic differential equations (SDEs) in the literature have a superlinearly growing
nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the …

In his forward-looking paper [374] at the conference “Mathematics Towards the Third
Millennium,” our esteemed colleague at Brown University Prof. David Mumford argued that …

A new class of explicit Euler schemes, which approximate stochastic differential equations
(SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It …

A version of the fundamental mean-square convergence theorem is proved for stochastic
differential equations (SDEs) in which coefficients are allowed to grow polynomially at …

We are interested in the strong convergence and almost sure stability of Euler–Maruyama
(EM) type approximations to the solutions of stochastic differential equations (SDEs) with …

We are interested in strong approximations of one-dimensional SDEs which have non-
Lipschitz coefficients and which take values in a domain. Under a set of general …

We develop a perturbation theory for stochastic differential equations (SDEs) by which we
mean both stochastic ordinary differential equations (SODEs) and stochastic partial …

Since Giles introduced the multilevel Monte Carlo path simulation method [18], there has
been rapid development of the technique for a variety of applications in computational …