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.

This is the expanded second edition of a successful textbook that provides a broad introduction to the important area of stochastic modelling. The original text had been developed from lecture notes for a one-semester course on the topic for third-year science and actuarial students at the University of Melbourne. It reviews the basics of probability theory, and then covers 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. Rigorous proofs are often replaced with sketches of arguments with indications as to why a particular result holds, and also how it is connected to other results and illustrated by well-selected examples. Wherever possible, the book includes references to more specialised texts containing both proofs and more advanced material related to the topics covered.