Informal Introduction To Stochastic Calculus With Applications, An by Ovidiu Calin (PDF)

Description

The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author aims to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.

User’s Reviews

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

⭐The advertisement for this book is very misleading. It starts in a simple way to fool you and quickly dives into Mathematical jargon that leaves you grasping for air. You definitely need a lot more than just undergraduate calculus.

⭐EDIT: THERE’S A 2ND EDITION OF THE BOOK THAT DOESNT GET ADVERTISED, GO SEARCH FOR THAT ONE INSTEAD!!tl;dr: great, great book that makes the subject very digestible. But it is not without its faults.I have been reading this book for at least a few months now and I have a ton to say about this book.I have a love hate relationship with this book because it attempts to bring the user to understand Stochastic Calculus with little to no knowledge of advanced mathematics. The author heavily implies that the prerequisite is only Calculus (Calculus 1-3 by the way). I am not sure if I would have been able to read this book after taking just my calculus sequence.What I love about the book:-It is mostly straight forward and clear.This book is not perfect, but it is sufficient for me at my level of mathematical knowledge. I would say that if you are serious about learning the subject and have some familiarity with “proof based” math work then you could probably pick this book up. If you do have just calculus just take the book for what it is and reference other sources if you need it.-It does not assume knowledge of probability.I would have liked if the author had explicitly stated the prerequisites but I recommend you have some knowledge of probability and statistics before picking up this book. If not then you should be okay anyways, but literally anything helps. Even your business stats class is useful.-Introductory section on measure theoretic probability.This is section is good, it’s somewhat similar to chapter 2 of Klebaner’s book but this is actually useful. It does a good, almost great job of teaching probability and I love it. This chapter is so important I would have loved some real world examples to really have the ideas stick (i.e. computational exercises and examples). The author does this in the second half of the book I am not sure why he didn’t do it in the first part. I would still recommend having a couple of references near by (Mikosch and Shreve)-There are solutions to many problems.ACTUALLY solutions. Most of them are useful and help a lot. A few are not so useful and are useless.My issues with this book are:-The author uses mathematical jargon (at least) a few times without stating their definitions beforehand.A possible audience for this text are business majors. Do business majors know what compact interval, hilbert spaces, and square integrable mean? Some might, but many probably don’t. It can be disheartening to see all this terminology being thrown around without a definition first. Square integrable is used and then defined officially two pages later, while Hilbert Space is only slightly hinted at what its definition is.-Several exercises should be examples/needs more examples.Some of these exercises should really be examples to really ensure understanding. I would like some more computational examples in the book since it really is “informal”. If you disagree then that’s fine because some of the exercises in which we are asked to show or prove a result should be examples as well!-Some of the solutions have typos, but not many.mostly in the beginning of the solutions for the second chapter.-Some solutions need more detail, some are almost useless.-Many exercises build off each other.This is a pet peeve of many people and it can be annoying. Especially if you are going to pick and choose which exercises to and not to do you may have a hard time. The upside to this is that there are solutions, but again, not to every problem.-Theorems/techniques are used in exercises without having been used before.Now I can understand this from a graduate level textbook on Analysis or something, but in a book like this… I don’t know man you’re gonna have a hard time convincing me that a business major is going to invoke the squeeze theorem without having first seen it in the text.I would say that the text really comes into its own after the third chapter. The author really went out of his way to make the stochastic calculus parts of the book very digestible. The first few chapters of preliminary information do not have exercises and examples in the same way as in the second half of the book. In the second half there are many computational exercises and examples and they really help.I understand that the author has taken a very special “easy” approach in this book, but the sections on stochastic calculus are made very very simple and straightforward. He definitely could have made the earlier sections on probability that much simpler as well by taking a similar approach.If you’re looking to get into the subject and you don’t have analysis or probability under your belt then I recommend the book. If you have both of those then there are probably better books for you at your level. But then this one might be easy for you. I like the book a lot, but I also hate certain aspects of it a lot. It is frustrating because with a little bit of tweaking it could be one of the best books on the subject at this level.

⭐From all the books on stochastic calculus I have seen, this is definitely the best one. Although the first 5 chapters are a bit heavy on the pure mathematics side (mainly rigorous proofs and theorems), I found chapters 6 – 11 to be particularly useful, especially with the inclusion of worked examples on how to evaluate stochastic integrals using the Ito formula, expectation and variance of stochastic processes, and apply these concepts to the solution of stochastic differential equations. It is concise, but you may have to do a little bit of reading between the lines to grasp every concept fully. If you are looking for a book that shows you how to solve problems in stochastic calculus rather than using the word “martingale” in every sentence, then look no further.

⭐The ideal starting point for every economics/finance student. The book presents concepts in a very simple manner without obfuscating the key points, lots of exercise (with complete solutions!) are available to test your skills. Highly recommended!

Keywords

Free Download Informal Introduction To Stochastic Calculus With Applications, An in PDF format
Informal Introduction To Stochastic Calculus With Applications, An PDF Free Download
Download Informal Introduction To Stochastic Calculus With Applications, An 2015 PDF Free
Informal Introduction To Stochastic Calculus With Applications, An 2015 PDF Free Download
Download Informal Introduction To Stochastic Calculus With Applications, An PDF
Free Download Ebook Informal Introduction To Stochastic Calculus With Applications, An