Introduction to Stochastic Processes Using R

This textbook presents some basic stochastic processes, mainly Markov processes. It begins with a brief introduction to the framework of stochastic processes followed by the thorough discussion on Markov chains, which is the simplest and the most important class of stochastic processes. The book then elaborates the theory of Markov chains in detail including classification of states, the first passage distribution, the concept of periodicity and the limiting behaviour of a Markov chain in terms of associated stationary and long run distributions. The book first illustrates the theory for some typical Markov chains, such as random walk, gambler's ruin problem, Ehrenfest model and Bienayme-Galton-Watson branching process; and then extends the discussion when time parameter is continuous. It presents some important examples of a continuous time Markov chain, which include Poisson process, birth process, death process, birth and death processes and their variations. These processes play a fundamental role in the theory and applications in queuing and inventory models, population growth, epidemiology and engineering systems. The book studies in detail the Poisson process, which is the most frequently applied stochastic process in a variety of fields, with its extension to a renewal process.

The book also presents important basic concepts on Brownian motion process, a stochastic process of historic importance. It covers its few extensions and variations, such as Brownian bridge, geometric Brownian motion process, which have applications in finance, stock markets, inventory etc. The book is designed primarily to serve as a textbook for a one semester introductory course in stochastic processes, in a post-graduate program, such as Statistics, Mathematics, Data Science and Finance. It can also be used for relevant courses in other disciplines. Additionally, it provides sufficient background material for studying inference in stochastic processes. The book thus fulfils the need of a concise but clear and student-friendly introduction to various types of stochastic processes.

Sivaprasad Madhira has been Lecturer and Reader in the Department of Statistics, University of Pune, India; Professor of Statistics and Head, Department of Computer Science, Shivaji University, Kolhapur; Professor of Computer Applications, SIBER, Kolhapur; Director (MCA) and Director (IMED), Dean (Faculty of Management Studies) at Bharati Vidyapeeth University, Pune. He retired as Professor, Computer Applications, at IMED and Director - ICT at Bharati Vidyapeeth University, Pune. At present he is a visiting faculty at Savitribai Phule Pune University, formerly known as University of Pune. Prof. Prasad has started new departments/new programs and conducted quality courses in Statistics, Computer Science and Management. He was instrumental in setting up the statistics program and MCA program at Shivaji University; MCA program at SIBER, Kolhapur; and MCA program at Bharati Vidyapeeth University. During his career spanning 49 years of teaching and research, he has published many research papers in national and international journals of repute and supervised students for their PhD and MPhil degrees. He participated in numerous national and international conferences and delivered invited lectures.

Shailaja Deshmukh, retired as Professor of Statistics from the Department of Statistics, Savitribai Phule Pune University, formerly known as University of Pune, India, and continues to serve there as a visiting faculty. She has taught around twenty five different theoretical and applied courses. She worked as a visiting professor at the Department of Statistics, University of Michigan, Ann Arbor, Michigan during 2009-10 academic year. Her areas of interest are inference in stochastic processes, applied probability and analysis of microarray data. She has a number of research publications in various peer-reviewed journals. She has worked as an executive editor and as a chief editor of the Journal of Indian Statistical Association and is an elected member of the International Statistical Institute. She has authored five books --- ‘Microarray Data: Statistical Analysis Using R’ (jointly with Dr. Sudha Purohit) in 2007; ‘Statistics Using R’ (jointly with Dr. Sudha Purohit and Prof. Sharad Gore) in 2008; ‘Actuarial Statistics: An Introduction Using R’ in 2009; ‘Multiple Decrement Models in Insurance: An Introduction Using R’ in 2012; and ‘Asymptotic Statistical Inference: A Basic Course Using R’ in 2021; with the last two being published by Springer.