Rengarajan holds a Master of Financial Engineering - University of
California, Berkeley and he works in the investment management
industry and specializes in providing economic and investment outlook
and strategy for global equity and government bond markets. He has an
educational background in financial engineering, business, and
engineering, and professional interests include business,
finance, economics, technology and related areas.
Authors: Liliana Blaco Castaneda,
Viswanathan Arunachalam, Selvamuthu Dharmaraja
Modeling of random processes is essential in several fields including manufacturing, bio sciences, and business to name a few and a solid understanding of probability theory forms the basis of modeling random processes. The book aims to provide a solid but easy to understand treatment of the subject for a beginner.
The introduction gives a brief overview of the subject as well as the history and provides the motivation behind studying probability theory.
Basic concepts starts with definitions for probability space and theorems, conditional probability and event independence. In this way, the book does not assume any background in the subject. The general math pre-requisites such as linear algebra, set theory, and combinatorics are covered briefly in the appendix.
The chapter on random variables and distributions describe a whole ranges of both discrete and continuous random variables including basic definition and their properties.
Within discrete distributions, the book covers the binomial, hypergeometric, poisson and geometric distributions and within continuous distributions, the book covers normal, gamma and beta distributions.
In addition to just describing the general properties of the distribution the part on relationships between distributions gives a great overview to see how the different distributions are connected. The examples and exercises cover a whole range of applications.
The joint distribution of random variables is then covered followed by a really useful concept of probability theory - conditional expected values.The section on multivariate normal distribution and properties includes standard basic treatment of the means, variances and covariances.
Limit theorems cover the theory about how to draw conclusions about populations from a sample and to quantify how reliable the conclusions are. The chapter goes on to the weak and strong laws of large numbers, markov and chebyshev inequalities, and chebyshev’s theorem - one of the most important results in probability theory.
The final chapters are a quick introduction to concepts which are targeted towards students of math finance. The introduction to stochastic processes covers basics such as stationary processes, independent and stationary increments, markov chains and poisson processes.
Queueing models deal with basic markovian single and multi server models as well as a brief discussion on non markov models, while the chapter on stochastic calculus deals with martingales and brownian motion.
Throughout the book there are a variety of examples to link theory to practise. The exercise list at the end of each chapter is exhaustive and provides adequate drill in helping to understand concepts.
The book clearly meets its goal of providing a clear and solid introduction to probability theory and stochastic processes. The simple style and orientation towards putting concepts to practise make this as a good book for a practitioner.