In recent years, random variables and stochastic processes have emerged as important factors in predicting outcomes in virtually every field of applied and social science. Ironically, according to Nicolas Bouleau and Dominique Lepingle, the presence of randomness in the model sometimes leads engineers to accept crude mathematical treatments that produce inaccurate results. The purpose of Numerical Methods for Stochastic Processes is to add greater rigor to numerical treatment of stochastic processes so that they produce results that can be relied upon when making decisions and assessing...

The book deals with propagation of errors on data through mathematical models with applications in finance and physics. It is interesting for scientists and practitioners when studying the sensitivity of their models to small changes in the hypotheses. The book differs from what is usually done in sensitivity analysis because it yields powerful new tools allowing to manage errors in stochastic models as those used in modern finance.

A simplified approach to Malliavin calculus adapted to Poisson random measures is developed and applied in this book. Called the "lent particle method" it is based on perturbation of the position of particles. Poisson random measures describe phenomena involving random jumps (for instance in mathematical finance) or the random distribution of particles (as in statistical physics). Thanks to the theory of Dirichlet forms, the authors develop a mathematical tool for a quite general class of random Poisson measures and significantly simplify computations of Malliavin matrices of Poisson...