The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations, due to the peculiarities of stochastic calculus. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. To help the reader develop an intuitive understanding and hands-on numerical skills, numerous exercises and PC-Exercises are included. The book is directed at a multi-disciplinary readership, consisting primarily of engineers, financial analysts, physicists and mathematicians developing numerical schemes for applications of SDEs, and also of researchers in other fields like biology, chemistry or economics who, with less mathematical background, wish to apply

1. Probability and Statistics.- 2. Probability and Stochastic Processes.- 3. Ito Stochastic Calculus.- 4. Stochastic Differential Equations.- 5. Stochastic Taylor Expansions.- 6. Modelling with Stochastic Differential Equations.- 7. Applications of Stochastic Differential Equations.- 8. Time Discrete Approximation of Deterministic Differential Equations.- 9. Introduction to Stochastic Time Discrete Approximation.- 10. Strong Taylor Approximations.- 11. Explicit Strong Approximations.- 12. Implicit Strong Approximations.- 13. Selected Applications of Strong Approximations.- 14. Weak Taylor Approximations.- 15. Explicit and Implicit Weak Approximations.- 16. Variance Reduction Methods.- 17. Selected Applications of Weak Approximations.- Solutions of Exercises.- Bibliographical Notes.