This paper gives a review of recent progress in the design of numerical methods for
computing the trajectories (sample paths) of solutions to stochastic differential equations. We …

Classically, the continuous-time Langevin diffusion converges exponentially fast to its
stationary distribution π under the sole assumption that π satisfies a Poincaré inequality …

Monte Carlo methods are a very general and useful approach for the estimation of
expectations arising from stochastic simulation. However, they can be computationally …

These lecture notes highlight the mathematical and computational structure relating to the
formulation of, and development of algorithms for, the Bayesian approach to inverse …

Stochastic differential equations (SDEs) and the Kolmogorov partial differential equations
(PDEs) associated to them have been widely used in models from engineering, finance, and …

This textbook provides the first systematic presentation of the theory of stochastic differential
equations with Markovian switching. It presents the basic principles at an introductory level …

In financial and actuarial modeling and other areas of application, stochastic differential
equations with jumps have been employed to describe the dynamics of various state …

During the seven years that elapsed between the first and second editions of the present
book, considerable progress was achieved in the area of financial modelling and pricing of …

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 …

Influenced by Higham et al.(2003), several numerical methods have been developed to
study the strong convergence of the numerical solutions to stochastic differential equations …