An Informal Introduction to Stochastic Calculus with Applications

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 Problems
• Basic Notions
• Useful Stochastic Processes
• Properties of Stochastic Processes
• Stochastic Integration
• Stochastic Differentiation
• Stochastic Integration Techniques
• Stochastic Differential Equations
• Applications of Brownian Motion
• Girsanov's Theorem and Brownian Motion
• Some Applications of Stochastic Calculus
• Hints and Solutions

Readership: 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 understanding
• The 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 understanding
• The 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