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Suggestion for a probability theory book

Hi guys,

I completed solving the first five chapters(construction of reals, sequences and series, basic topology of [imath]\mathbf{R}[/imath], functional limits and continuity, the derivative) from an elementary undergrad analysis book, Understanding Analysis, by Stephen Abbott.

Any recommendations for (i)probability theory and (ii)measure theory book(s) that could be a natural progression to Abbott? I have been suggested Probability w/ Martingales by David Williams (does not pre-suppose any measure theory).

Cheers,
Quasar.
 

Daniel Duffy

C++ author, trainer
Cheap at half the price, is it serious .. 25.95 Euro for a chapter????

BTW wasn't this topic already discussed here several times?
 
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Cheap at half thee price, is it serious .. 25.95 Euro for a chapter????

BTW wasn't this topic already discussed here several times?
I didn't see as carefully; I have a copy which I purchased for a very affordable price at Amazon.

I searched some previous posts here, but those are more Ross-style books. I'd want to try and learn some probability theory, based on my limited experience with elementary analysis.
 
Maybe book by Sean Dineen?
Sean Dineen is from the University of Dublin! His book is very unique. I read about it on the MAA website. I anyway plan to use this - do you think I should supplement it with something?

Probability Theory in Finance: A Mathematical Guide to the Black-Scholes Formula | Mathematical Association of America
 
Dineen is a good book but I can't recommend it for learning probability and acquiring computational skill. Likewise for Williams. Do you already have a background in non-measure-theoretic probability? That's arguably the first priority.
 
Dineen is a good book but I can't recommend it for learning probability and acquiring computational skill. Likewise for Williams. Do you already have a background in non-measure-theoretic probability? That's arguably the first priority.
I have some background of calculus based probability - combinatorics, conditional probability and Bayes, discrete distributions - binomial, geometric & hypergeometric, continuous ones - expo, gaussian, poisson, moments.

I haven't read an elementary probability book from cover to cover. I have managed to solve the first eight chapters of Feller's volume I, which only deals with discrete RV and was hoping that reading both the volumes would fill any gaps.
 
A couple I might suggest are

1) "Measure, Integral, and Probability" by Capinski and Kopp (everything by Capinski is well-written), and, at a greater level of sophistication

2) "An Introduction to Measure-Theoretic Probability" by Roussas.
 

Daniel Duffy

C++ author, trainer
Quasar is not the first to have issues with understanding measure theory and its applications to finance. My understanding of the mismatch between theory and practice is caused by:

1. Authors tend to be pure mathematicians who seem to have little interest in/knowledge of the applied and computational aspects of MT, the exception being Kloeden and Platen.
2. MT cannot be learned as a 2-page afterthought in finance books. Ideally, it takes 2-3 years in a pure maths degree programme to do it properly.
3. In practice, things end up in a computer as numerical algorithms.

Just writing the GBM SDE on the whiteboard again and again is not very illuminating.

//

The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites.
Paul Halmos

This quote could be reviewed in the current case.
 
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Daniel Duffy

C++ author, trainer
In an attempt to predict the future, a good knowledge of probability and measure could be a prerequisite for Functional Analysis and Machine Learning applications.

Would Leonhard Euler be a C++ programmer were he alive today? Imagine implementing Euler's method?
 
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Daniel Duffy

C++ author, trainer
In an attempt to predict the future, a good knowledge of probability and measure could be a prerequisite for Functional Analysis and Machine Learning applications.

Would Leonhard Euler be a C++ programmer were he alive today? Imagine implementing Euler's method?
This book looks kind of interesting as an application area of probability.

 
In an attempt to predict the future, a good knowledge of probability and measure could be a prerequisite for Functional Analysis and Machine Learning applications.

Would Leonhard Euler be a C++ programmer were he alive today? Imagine implementing Euler's method?
Okay, isn't functional analysis about studying functions between abstract spaces like Banach spaces, hilbert spaces... Why do you say, PT(probability theory) is a pre-requisite - or what are some connections? Just inquisitive.
 
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