Problems and Solutions in Stochastic Calculus with Applications exposes readers to simple ideas and proofs in stochastic calculus and its applications. It is intended as a companion to the successful original title Introduction to Stochastic Calculus with Applications (Third Edition) by Fima Klebaner. The current book is authored by three active researchers in the fields of probability, stochastic processes, and their applications in financial mathematics, mathematical biology, and more. The book features problems rooted in their ongoing research. Mathematical finance and biology feature pre-eminently, but the ideas and techniques can equally apply to fields such as engineering and economics.

The problems set forth are accessible to students new to the subject, with most of the problems and their solutions centring on a single idea or technique at a time to enhance the ease of learning. While the majority of problems are relatively straightforward, more complex questions are also set in order to challenge the reader as their understanding grows. The book is suitable for either self-study or for instructors, and there are numerous opportunities to generate fresh problems by modifying those presented, facilitating a deeper grasp of the material.

Contents:

• About the Authors


• Introduction


• Preliminaries from Calculus


• Concepts of Probability Theory


• Basic Stochastic Processes


• Brownian Motion Calculus


• Stochastic Differential Equations


• Diffusion Processes


• Martingales


• Semimartingales


• Pure Jump processes


• Change of Probability Measure


• Applications in Finance


• Applications in Biology


• Index

Readership: This book is aimed at those seeking to gain a grounding in the fields of probability, stochastic processes, stochastic calculus, mathematical finance, mathematical biology. As such is it suitable for researchers, undergraduate and graduate students in the above fields and is suitable for self-study or course adoption.

Key Features:

• Accessible to those new to the subject, unlike many other books on stochastic calculus which are usually very technical and not accessible to students without a solid mathematical background


• Companion volume to the successful Introduction to Stochastic Calculus with Applications (Third Edition) by Fima Klebaner


• Emphasises learning by example to enhance understanding


• It contains a few challenging questions, but most of the material is quite straightforward