Stochastic Calculus: An Introduction Through Theory and Exercises (Universitext)
Provides a self-contained introduction to stochasticcalculusIncludes applications and numerical methodsFeatures more than 200 exercises with detailed solutions——————————This book provides a comprehensive introduction to the theory ofstochastic calculus and some of its applications. It is the onlytextbook on the subject to include more than two hundred exerciseswith complete solutions.After explaining the basic elements of probability, the authorintroduces more advanced topics such as Brownian motion,martingales and Markov processes. The core of the book coversstochastic calculus, including stochastic differential equations,the relationship to partial differential equations, numericalmethods and simulation, as well as applications of stochasticprocesses to finance. The final chapter provides detailed solutionsto all exercises, in some cases presenting various solutiontechniques together with a discussion of advantages and drawbacksof the methods used.Stochastic Calculus will be particularly useful toadvanced undergraduate and graduate students wishing to acquire asolid understanding of the subject through the theory andexercises. Including full mathematical statements and rigorousproofs, this book is completely self-contained and suitable forlecture courses as well as self-study.