Stochastic Equations for Complex Systems

This book provides a better understanding of random dynamical systems and stochastic differential equations. It offers fundamental ideas and tools for the modeling, analysis, and prediction of complex phenomena.§The first part presents theoretical topics providing fundamental ideas and tools for the understanding of the computational topics. First, an introduction to stochastic differential equations and their different type of solutions is presented. The second chapter discusses an introduction to the Malliavin calculus and the Skorohod integral. And third, Monte Carlo methods is introduced in conjunction with a detailed mathematical justification.§The second part discusses the mathematical nature of multi-scale models. It further presents applications of molecular stochastic models to represent the Navier-Stokes equations. Finally, the application of stochastic methods to large-scale Monte Carlo turbulent flow simulations are introduced.§The book covers many relevant applications ranging from pure to applied, in particular, to turbulent flow simulations. It is primarily oriented towards PhD students, young and experienced researchers and professionals working in the area of stochastic differential equations and their applications.