Basic Stochastic Processes: A Course Through Exercises (Springer Undergraduate Mathematics Series) by Zdzislaw Brzezniak (PDF)

Description

Stochastic processes are tools used widely by statisticians and researchers working in the mathematics of finance. This book for self-study provides a detailed treatment of conditional expectation and probability, a topic that in principle belongs to probability theory, but is essential as a tool for stochastic processes. The book centers on exercises as the main means of explanation.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The notation is awful, and it seems like there’s purposeful obfuscation of the material. In particular, it assumes a familiarity with set theory and measure theory that is beyond most undergraduates (including math majors, at least at my school). The first two chapters present an overview of some results in probability rederived for the purposes of the rest of the book’s content. However, all the physical intuition seems to have been removed. It would have been better had it compared its derivations and results to the ‘usual’ approach without all the abstract math. I almost managed to UNLEARN probability theory.The only reason it’s got 2 stars is because once I struggled through understanding this particular formulation of probability theory (mostly thanks to the professor of the course expanding on the material), I am now more comfortable with the definition of a random variable.I hope there are other books on Stochastic Processes that offer a longer, gentler introduction to these topics and the notation, or otherwise better map out the required prerequisites.

⭐Well motivated; well explained; easy to understand! A great read; and still offering readers getting a deeper understanding! There are a number of reasons for this book: An understandable presentation of tools from probability and stochastic processes is especially timely.With clear explanations, and with lots of examples and illustrations!A useful first book, before turning to more specialized presentations!While the subject has a long history and a multitude of applications, there is more recent buzz: It has been suggested that the recent turmoil in financial markets may be caused in part by poor understanding on the part of traders of the mathematical models for derivative trading.The mathematical tools are widely used, but probably a lot less widely understood!A bit of history: Stochastic processes is a theory started more than a hundred years ago (1900, Louis Bachlier, a Paris-PhD thesis under Poincare), then Albert Einstein’s 1905 discovery of Brownian motion, Norbert Wiener’s path-space integral (the 1920ties), K. Ito’s integral & formula (the 1940ties) and Paul Samuelson-Merton-Black-Scholes 1974, a stochastic differential equation for option pricing: All mathematical tools devised for the purpose of predicting uncertain outcomes in the world around us: in financial engineering; in physics (quantum mechanics, diffusion & thermodynamics); in biology, and in other parts of our experience.Review by Palle Jorgensen, March 2010.

⭐The first four chapters are phenomenal. I simply love the way those concepts are presented. However, there is a noticeable style change starting from chapter 5 (since there are two authors, I guess). The writing of the main text and solutions becomes increasingly sloppy.

⭐This book is great to learn Stochastic Processes. The exercises are not too hard that one is discouraged at learning the topic, and the material covered is great.I do not give it 5 stars because I wish it went just that little bit beyond – I am not sure this is sufficient to embark upon reading Karatzas and Shreve for example.

⭐Stochastic process and measure theory is a hard topic. Yet this book presents it in a concise, self-containing, accurate way. It covers the core ideas of this field and illustrates them clearly. As a non-math science student, I find this book very readable and helpful.

⭐Excelent book. It has a lot of examples and excersices but the best thing is that all of them are resolved. This is a very important characteristic of this book. You can practice a lot but if you don’t have a clue and don’t have the help of your teacher maybe you can being losing your time. But no, this book is very different from anothers and it is perfect for people who likes to learn by themself and obviously it is perfect for a text book in a class. One thing in cos about this book is in the part of brownian motion the authors don’t much pay attetion to explain the intuative idea behind the brownian motion and this is very sad and bad. The number of pages of this book are short and maybe this is the reason why the authors don’t take much time to explain all the thing in a very good sense. I would like that oll the book were written like they.Buy this book without doubt.cheers from Lima Perú

⭐I am giving this book two stars based on its usefulness for me. I am wading through the book now, and it’s going very slowly.I made the mistake of equating teaching stochastic processes through exercises as meaning that those exercises were application oriented. It turns out that there is very little application in the book at all, so I am having a hard time with it.I just wanted to warn other business academics (and non-mathematicians in general) who might be tempted to make the foray into stochastic processes by way of this book. Despite brief opening remarks in each chapter about where these concepts might be applied, you’re pretty much left on your own to imagine how. Plus, you need to realize that it’s written for someone who came up through the ranks as a mathematician, not a (albeit quantitatively oriented) business scholar.

⭐It is difficult to study Stochastic Calculus without Measure Theory.I would not hesitate to recommend this book to students or new comers to the area. I think that this book would work well with David Williams’ Probability with Martingales.The authors aim at final year students. I think that is sensible, although 50 years ago when I was a student the material could have been dealt with by second year students! This is an excellent book.

⭐it is a good book and provide explanation. there is one thing to note though, this book requires a bit of real analysis.

⭐the content is perfect . But the quality of printing is just so so, because it was printed by Amazon.ac.uk, Ltd , not the originate publisher

⭐Excellent introduction to stochastic processes.

⭐Dieses Buch ist eine sehr gute Einführung in die komplexe Theorie der stochastischen Prozesse. Die Beispiele sind relativ einfach gestaltet, sodass sie für die meisten Leute mit mathematischem Grundwissen aus ca. 2 Semestern Mathematik oder Physik Vorlesungen lösbar sein sollten. Wer trotzdem bei einem Beispiel hängt, findet am Ende jedes Kapitels Lösungen, was auch keine Selbstverständlichkeit ist. Wer aus der Wirtschaft kommt und bisher kaum mit Beweisen zu tun gehabt hat, wird eher enttäuscht sein, da dieses Buch keine Applikationen aus der Finanzwelt bietet und das Thema nur aus einer theoretischen mathematischen Perspektive betrachtet. Das Beherrschen der Wahrscheinlichkeitstheorie ist ein großes Plus, wobei das nötigste Wissen (Borelmengen, Sigmaalgebren, Messbarkeit, etc.) daraus ebenfalls im ersten Kapitel abgedeckt ist. Für mich als Mathematik Student im 4. Semester war dieses Buch eine große Hilfe, da man sich damit die Theorie ohne Probleme autodidaktisch beibringen kann und sich eine gute Basis für schwierige Vorlesungsskripten schafft.Einen Punkt Abzug bekommt das Buch für die Ebook Version. Auf meinem Computer ist zwar alles gut lesbar, allerdings werden die Formeln auf der Kindle App auf meinem 8 Zoll Android Tablet sehr klein dargestellt und skalieren nicht mit der Schrift mit (bleiben also klein). Außerdem werden am Tablet bestimmte Zeichen nicht dargestellt (Reelle und Natürliche Zahlen), die sich allerdings aus dem Zusammenhang ergeben.

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