This text is an introduction to the modern theory and applications of probability and stochastics. The style and coverage is geared towards the theory of stochastic processes, but with some attention to the
applications. In many instances the gist of the problem is introduced in practical, everyday language and then is made precise in mathematical form.
The first four chapters are on
probability theory: measure and integration, probability spaces, conditional expectations, and the classical limit theorems. There follows chapters on martingales, Poisson random measures, Levy Processes, Brownian motion, and
Markov Processes.
Special attention is paid to Poisson random measures and their roles in regulating the excursions of Brownian motion and the jumps of Levy and Markov processes. Each chapter has a large
number of varied examples and exercises.
The book is based on the author's lecture notes in courses offered over the years at Princeton University. These courses attracted graduate
students from engineering, economics, physics, computer sciences, and mathematics.
Erhan Cinlar has received many awards for excellence in teaching, including the President's Award for
Distinguished Teaching at Princeton University. His research interests include theories of Markov processes, point processes, stochastic calculus, and stochastic flows. The book is full of insights and observations that only a
lifetime researcher in probability can have, all told in a lucid yet precise style.
Industry Reviews
From the reviews: "This excellent book aims to provide a bridge from ... classical stochastic process theory to the more abstract modern theory as it is developed and displayed in contemporary research monographs. ... Chapters are organized with the more accessible material at the beginning ... and preceded by appropriate heuristics and motivating ideas. ... It includes a good bibliography, which is referenced in the Notes and Comments section ... . Overall, this is a volume which any probabilist would be happy to add to their library." (David Stirzaker, SIAM Review, Vol. 54 (1), 2012) "This advanced textbook contains material for a two-semester course, based on what the author has taught at Princeton University. Each chapter begins with a pithy summary of what is to come; exercises ... are scattered throughout the text, and any reader with the stamina to work conscientiously through even most of this book will find their understanding of the area greatly enhanced. ... The author deserves congratulations for a masterly account of the fields covered ... ." (John Haigh, The Mathematical Gazette, Vol. 96 (536), July, 2012)
