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I am interested in exploring the new functionality on random processes available in Mathematica 9, but I am not familiar with all of the underlying mathematics.

Could you recommend a book that provides a foundation on these topics?

I am thinking about a book that favors intuition and breadth over proofs. I have an engineering background (and know probability and statistics decently well) and would like to rapidly take advantage of these functions. I am interested in both modeling and estimation issues.

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You can have a look at books on quantitative finance by Wilmott. –  b.gatessucks Dec 26 '12 at 9:55
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Also: amazon.com/… –  Chris Degnen Dec 26 '12 at 12:58
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if you prefer a more natural science-oriented approach, this might be interesting. My personal favourite would be van Kampen's book but that is less formal (and more opinionated). In any case, both are less formal than is usual in other disciplines. –  acl Dec 26 '12 at 13:17
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For a really unique approach to stochastics and probability, try: bergner.se/DMP . –  Vince Dec 26 '12 at 21:42
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up vote 5 down vote accepted

Introduction to Probability Models by Ross gives good description of stochastic processes. Applied Intertemporal Optimization by Walde also has easy to follow structure on stochastic models in both discrete and continuous time and it is free to download pdf.

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Ah good, someone remembered Ross. I wanted to add it, but my books are packed and I could not remember his name. +1 –  rcollyer Dec 27 '12 at 4:30
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