Help with probability books

cstassen · 7/13/08

Hi guys

I need to read some more probability, and maybe do a course or so in this. I need your help to select the book(s). I have the ones below to choose from. If anyone know one/more of the books, could you please indicate the level?

These should be pretty introductory:

E. Cinlar , Introduction to Stochastic Processes
S. Ross , Introduction to Probability Models
S. Karlin & H. Taylor , A First Course in Stochastic Processes
Grimmett and Stirzaker , Probability and Random Processes
H. M. Taylor and S. Karlin , An Introduction to Stochastic Modeling (3rd Edition)

These should be harder:

E. Cinlar , Lecture Notes on Probability
Neveu , Foundations of Calculus of Probabilities
Chung , A Course in Probability Theory
Breiman , Probability

IlyaKEightSix · 7/13/08

Try Grinstead and Snell's Intro to Probability. You can google the PDF for free.

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cstassen · 7/13/08

What is the level of that book?

I allready have a pretty large knowledge about probability. I have done introductory courses (courses introducing mean, variance etc) and intro. stat courses (testing, distributions etc). I have also done more advanced courses, with probability on a measure theoretical base, so I have an ok knowledge of measure theory (could be better though), and have seen some pretty advanced prob. I have also seen martingales and brownian motions on introductory level. I have also done analysis.

I'm looking for something building on top of this.

Minh Tran · 7/13/08

Suppose that you're interested in FE.

"Measure, Integral and Probabilities" <~ Since you have a good basic knowledge, this may help you for the combination between Prob and Analysis (even application in Math Fin ^^)

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Bastian Gross · 7/13/08

I warmly recommend both books by Karlin & Taylor.
Furthermore you should read Protter "Stochastic Integration and Differential Equations".

It is a remote possibility to google this book for free.

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cstassen · 7/13/08

Thanks Mihn and Bastian. Yes, I'm into FE. What about the level of the books? Are they suitable for me you think?

The thing is, that I'm doing a master next year, and I have to do a course in probability. There are two courses to chose from, and I'm trying to asses which is the right for me. The above books belongs to the "easy" one, the below to a harder course. I want to go for the "hard" course, but do you think thats possible for me?

bigbadwolf · 7/15/08

One book I've recently bought is Allan Gut's An Intermediate Course in Probability. This is pitched at a level between intro books like Ross and grad-level measure-theoretic treatments like Shiryaev and Kallenberg. It's expensive for what it is: $75 for a 280-page paperback. But I don't know any other book like this.

One other book I want to recommend in passing is Shafer and Vovk's Probability and Finance.

For Brownian motion, the single best text I know (and by now I know dozens) is Wiersema's Brownian Motion Calculus.

If you alread know the contents of the first volume of Karlin and Taylor, you have a pretty solid background in stochastic processes.

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cstassen · 7/15/08

bigbadwolf, thanks! - I have done measure theory, but it was in a european university, so it was an undergrad course. I therefore think it was at a level a little bit lower than american grad-courses introducing measure theory (although not much).

Do you think that I will be able to follow the hard course (the one using the books below) with my background in measure theory?

bigbadwolf · 7/15/08

cstassen said:
Do you think that I will be able to follow the hard course (the one using the books below) with my background in measure theory?

The problem is not in being able to follow the "hard" course: it's a piece of cake to follow any axiomatic development (which is precisely what happens in measure-theoretic probability). The problem is to understand the need for it. Why do we need measure theory as a foundation? In what way do our results become more general or more subtle? Can we do without it? Because the leap from undergrad probability to measure-theoretic probability is so great, students spend their time going over the technical details and language of the new measure-theoretic version, often without being able to tie it organically to what they did before, or to be able to think about it critically. This is where Gut's intermediate book comes in handy. Of the "hard" books you've listed, I only know the Chung book. You will be able to follow it. But you may not be able to see the wood for the trees for a while.

cstassen · 7/15/08

Thanks - that's exactly the kind of answer I was looking for. And yes, when I first saw measure theory I could see no use for it at all, but when I did my second course using it, it made more sense I think, and doing a third one should then - hopefully - make it even more clear!

What about the first course - do you think that will be "too easy"? (I guess any probability course is as hard as one makes it, but...)

bigbadwolf · 7/16/08

cstassen said:
What about the first course - do you think that will be "too easy"? (I guess any probability course is as hard as one makes it, but...)

Your interest in the subject -- if you have it -- will be the driving force. I personally tend to choose harder courses, often to my detriment, and it's a question of taste. Intro courses are often tedious and shallow. Advanced courses -- if well taught -- are more nuanced and offer a more panoramic and sophisticated point of view.

Were I you, I would find out what particular topics will be covered in each course and the nature of the presentation (if that's possible). And then let your interest in the subject make the decision for you.

cstassen · 7/19/08

By the way - if you didn't allready know - you can find many prob. notes at econphd.net - the ones you mention here are theere

const451 · 8/12/08

Someone could comment on Probability and Statistics by DeGroot?

THX

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bigbadwolf · 8/12/08

const451 said:
Someone could comment on Probability and Statistics by DeGroot?

Uninspired.

IlyaKEightSix · 8/12/08

Grinstead and Snell's Intro to Probability! You can find a PDF online for free since they're so filthy stinking rich off of the boook already!

ReBorn · 8/12/08

I would start with something like Resnick's Probability Path. There are also good books by Durrett, Ash, Gut. To learn the basics of stochastic differential equations check out Oksendal (a more advanced text on the topic is by Karatsaz and Shreeve).

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const451 · 8/13/08

DeGroot is not in favor... Unfortunately it is required for the course I am taking as a prereq. I am looking for another textbook as a supplement. Durrett, Ash, Gut are above the level I need; Resnick and Grinstead look alright.

What about the First Course in Probability by Sheldon Ross?

bigbadwolf · 8/13/08

const451 said:
What about the First Course in Probability by Sheldon Ross?

A standard text. Again, lacking the magic of inspiration. I don't know your level, but since you want a supplement to DeGroot, you must most probably be a beginner. One that I recommend is:

1) A Natural Introduction to Probability Theory, by Ronald Meester, pub. Birkhauser. This is a succinct 186-page paperback that will take a beginner to the stage where he's ready for a measure-theoretic approach to the subject (e.g. Kallenberg's Foundations of Modern Probability). An added benefit is the book isn't published by an American publisher, most of whom are money-gouging bandits.

Another I like, despite its venerable old age is:

2) An Introduction to Probability Theory and its Applications (Vol 1), by Feller, pub. Wiley.

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const451 · 8/13/08

Thanks a lot - that would be sufficient. Also, Statistics sequence is making sense to me now.

I also need recommendation on supplementary textbook in PDE... but I'd better create a new thread for that.

bigbadwolf · 8/14/08

Going through my stacks today, I came across another very good intro probability book:
The Probability Tutoring Book, by Carol Ash. Better than Ross.

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Help with probability books

cstassen

IlyaKEightSix

cstassen

Minh Tran

Bastian Gross

German Mathquant

cstassen

bigbadwolf

cstassen

bigbadwolf

cstassen

bigbadwolf

cstassen

const451

bigbadwolf

IlyaKEightSix

ReBorn

const451

bigbadwolf

const451

bigbadwolf

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