## Probability and Stochastics

Author(s):
Erhan Çinlar
Publisher:
Springer. Graduate Texts in Mathematics 261
Year:
2011
ISBN:
978-0-387-87858-4;e-ISBN: 978-0-387-87859-1; DOI 10.1007/978-0-387-87859-1; ISSN 0072-5285
Price (tentative):
Between 51.16€ (ebook)-62.35€
Short description:

The book is an introduction to the modern theory of probability and stochastic processes. It based on the lecture-notes for two-semester, fairly popular, which Prof. Çinlar, a well-known professor and researcher, at Princeton University,ecinlar$princeton.edu, has offered for many years. The course attracks graduate students in Business-Banking,computer sciences, engineering, eonomics, physics, finance, and mathematics and others related disciplines, and may be recommended to undergraduate students who are yet convinced that the mathematics appear in more places or in differents fields of knowledge, and also suitable for individual study. The style and coverage is directed toward the theory of stochastic processes and its applications. In many instances, the gist of the problems is introduced in every-day language and then all written in a precise matematical form. The first four chapters are in probability theory: measure and integration, probability theory, convergence and conditioning. There follows chapters on martingales and stochastics, Poisson random measures, Brownian motion and Markov Processes. The book is full of insights and observations that only a lifetime researcher in Probability and Stochastic Processes can have. URL for publisher, author, or book: http://w.w.w.springer.com/series/136;ecinlar$princeton.edu.
MSC main category:
60 Probability theory and stochastic processes
MSC category:
60-01;60A10;60B10;60C05;60F05;60G05;60J05;60H05
Other MSC categories:
60J65;60G45;60G46;60G48;60G51;60J75;60.60
Review:

The book is an introduction to the modern theory of probability and stochastic processes. It based on the lecture-notes for two-semester, fairly popular, which Prof. Çinlar, a well-known professor and researcher, at Princeton University,ecinlar@princeton.edu, has offered for many years.
The first four chapters are in probability theory: measure and integration, probability theory, convergence and conditioning.
The first chapter is a review of measure and integration in the context of the modern literatura on probability and stochastic processes. The second introduces probability spaces as espeila measure spaces.The chapter three is on convergence, routinely classical, and the chapter four in on conditional expectations included Radon-Nikodyn derivatives.
There follows chapters on martingales and stochastics, Poisson random measures, Brownian motion and Markov Processes.
Martingales are introduced in chapter V, the treatment of continuous martingales contain an improvement, achieved through the introductiion of a Doob martingale, a stopped martingale that is uniformly integrable. Two great theorems are considered:martingale characterization of Brownian motion due to Lévy and the characterization of Poisson process due to Watanabe.
Poisson random measures are in Chapter VI, the treatment is from the point of vue of their uses,specially,of Lévy processes. This chapter pays some attention to processes with jumps. The chapter VIII on Brownian motion is mostly on the standard material. Finally, the Chapter IX, on Markov processes, Itô diffusions and jump-diffusions are introduced via stochastic integral equations, as an integral path in a field of Lévy Proceses.
In short, the book is higher recommended. It provides new simple proofs of important results on Probability Theory and Stochastics Processes. In my opinion, it is a stimulating textbook will be for the teaching and research of the materia. A well written text with excellent tools for many instances, in every day language, and then all written precise in mathematical form.

Reviewer:
Francisco José Cano Sevilla
Affiliation: