• 1 Mean-square approximation for stochastic differential equations.- 2 Weak approximation for stochastic differential equations.- 3 Numerical methods for SDEs with small noise.- 4 Stochastic Hamiltonian systems and Langevin-type equations.- 5 Simulation of space and space-time bounded diffusions.- 6 Random walks for linear boundary value problems.- 7 Probabilistic approach to numerical solution of the Cauchy problem for nonlinear parabolic equations.- 8 Numerical solution of the nonlinear Dirichlet and Neumann problems based on the probabilistic approach.- 9 Application of stochastic numerics to models with stochastic resonance and to Brownian ratchets.- A Appendix: Practical guidance to implementation of the stochastic numerical methods.- A.1 Mean-square methods.- A.2 Weak methods and the Monte Carlo technique.- A.3 Algorithms for bounded diffusions.- A.4 Random walks for linear boundary value problems.- A.5 Nonlinear PDEs.- A.6 Miscellaneous.- References.

From the reviews of the first edition: "Milstein and Tretyakov's book is a significant contribution to stochastic numerics. It is essential reading for anyone with serious interest in the field, either theoretical or practical." (Mathematical Reviews, 2005) "The monograph presents research results of the authors concerning the numerical treatment of stochastic differential equations. ... The book is written in the style of a research exposition. It provides a rich source of mathematical theory, examples and insightful remarks and is thus essential material for those who are interested in the subject, from both a theoretical and practical viewpoint." (Evelyn Buckwar, Zentralblatt MATH, Vol. 1085, 2006)