An Informal Introduction to Stochastic Calculus with Applications (ePub)

The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author aims to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.Contents:A Few Introductory ProblemsBasic NotionsUseful Stochastic ProcessesProperties of Stochastic ProcessesStochastic IntegrationStochastic DifferentiationStochastic Integration TechniquesStochastic Differential EquationsApplications of Brownian MotionGirsanov's Theorem and Brownian MotionSome Applications of Stochastic CalculusHints and SolutionsReadership: Undergraduate and graduate students interested in stochastic processes.Key Features:The book contains numerous problems with full solutions and plenty of worked out examples and figures, which facilitate material understandingThe material was tested on students at several universities around the world (Taiwan, Kuwait, USA); this led to a presentation form that balances both technicality and understandingThe presentation mimics as close as possible the same chapters as in deterministic calculus; former calculus students will find this chronology of ideas familiar to Calculus