In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Ito integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view.
The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations."

The lecture courses of the CIME Summer School on Probabilistic Models for Nonlinear PDE's and their Numerical Applications (April 1995) had a three-fold emphasis: first, on the weak convergence of stochastic integrals; second, on the probabilistic interpretation and the particle approximation of equations coming from Physics (conservation laws, Boltzmann-like and Navier-Stokes equations); third, on the modelling of networks by interacting particle systems. This book, collecting the notes of these courses, will be useful to probabilists working on stochastic particle methods and on the approximation of SPDEs, in particular, to PhD students and young researchers.

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Children's CGI-animated adventure featuring the voice talents of Johnny Depp, Bill Nighy and Timothy Olyphant. Rango (voiced by Depp), a pet chameleon who has long harboured dreams of being a swashbuckling hero, is offered a chance to prove himself when he becomes stranded in the Mojave Desert after tumbling from his owner's car. Rango is guided to the nearby town of Dirt by friendly iguana Beans (Isla Fisher), where an act of accidental heroism earns him the respect of the town's residents and sees the Mayor (Ned Beatty) appoint him Sheriff. Top of Rango's priority list in his new position is to find out what is happening with the town's dangerously low water supply. He uncovers a conspiracy that goes right to the heart of the town's power structure; one that will require the intervention of a true hero to overturn. Is Rango up to the task? The movie won the 2012 Academy Award for Best Animated Feature Film.