ELEMENT OF STOCHA MODEL (3RD ED)

This is a thoroughly revised and expanded third edition of a successful university textbook that provides a broad introduction to key areas of stochastic modelling. The previous edition was developed from lecture notes for two one-semester courses for third-year science and actuarial students at the University of Melbourne.

This book reviews the basics of probability theory and presents topics on Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation. It also features elements of stochastic calculus and introductory mathematical finance. This makes the book suitable for a larger variety of university courses presenting the fundamentals of modern stochastic modelling.

To make the text covering a lot of material more appealing and accessible to the reader, 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. It is in this aspect that the present, third edition differs from the second one: the included background material and argument sketches have been extended, made more graphical and informative. The whole text was reviewed and streamlined wherever possible to make the book more attractive and useful for readers. Where appropriate, the book includes references to more specialised texts on respective topics that contain both complete proofs and more advanced material.

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 undergraduate students, graduate students, lecturers and researchers in mathematics, statistics, actuarial sciences and economics.

Review of the Second Edition:'This book is a very readable and comprehensive introduction to the most important topics of stochastic modeling. Each chapter also contains a section with recommended literature, so that a reader who becomes interested in certain topics can easily find more details and additional mathematical results.' - Mathematical Reviews Clippings

Reviews of the First Edition:The author is a well-known probabilist and now he is showing that he is also an excellent writer of a book for university students … in this book we find carefully selected topics from the area of stochastic modelling all presented in a masterful way. - Zentralblatt MATH

This is a very well-written brief introduction to stochastic modeling and related topics. This is a text that every professional in the field might want to consider adding to his bookshelf. For those instructors who like the choice of topics covered, it is also a nice candidate for a very advanced undergraduate or beginning graduate course in stochastic processes for students in various fields who have very good mathematical backgrounds and previous courses in probability theory. - The American Statistician

A fine pedagogical touch and a good sense of proportion make the text extremely well balanced. A very intelligent book indeed. - Acta Scientiarum Mathematicarum

Key Features:

• A well-written brief introduction to stochastic modelling and related topics
• The third edition contains explanations of rigorous proofs (which were omitted or mentioned briefly in previous editions) are expanded and made more graphical
• Aimed at advanced level undergraduate and introductory level graduate courses on stochastic modelling for students in various programs who would have a good mathematical background and previous courses in probability theory
• 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 two editions received very good reviews in professional journals and were adopted for a number of courses in universities around the world