Elements of Stochastic Modelling

This is the expanded second edition of a successful textbook that provides a broad introduction to important areas of stochastic modelling. The original text was developed from lecture notes for a one-semester course for third-year science and actuarial students at the University of Melbourne. It reviewed the basics of probability theory and then covered the following topics: Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation.

The present edition adds new chapters on elements of stochastic calculus and introductory mathematical finance that logically complement the topics chosen for the first edition. This makes the book suitable for a larger variety of university courses presenting the fundamentals of modern stochastic modelling. Instead of rigorous proofs we often give only sketches of the arguments, with indications as to why a particular result holds and also how it is related to other results, and illustrate them by examples. Wherever possible, the book includes references to more specialised texts on respective topics that contain both proofs and more advanced material.

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Contents:

• Introduction
• Basics of Probability Theory
• Markov Chains
• Markov Decision Processes
• The Exponential Distribution and Poisson Process
• Jump Markov Processes
• Elements of Queueing Theory
• Elements of Renewal Theory
• Elements of Time Series
• Elements of Simulation
• Martingales and Stochastic Calculus
• Diffusion Processes
• Elements of Mathematical Finance

Readership: Advanced undergraduates, graduate students, lecturers and researchers in mathematics, statistics, actuarial sciences and economics.
Key Features:

• The second edition contains two new and important chapters providing a gentle introduction and insight into stochastic calculus and mathematical finance
• An attractive option as a text on which a variety of modern courses for students majoring in science, electronic engineering, economics and actuarial science can be based
• The first edition of the text was met with very good reviews in professional journals and was adopted for a number of courses in universities around the world