I am looking for recommendations of a good first book to read on stochastic calculus / Itō calculus, say at the advanced undergraduate level. Does anyone have a favorite? Thanks so much!
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1Oksendal is popular - I forget the book title. – Paul Mar 13 '15 at 15:20
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2Thank you! I found it - for others searching this later, here's the link: http://www.amazon.com/Stochastic-Differential-Equations-Introduction-Applications/dp/3540047581 – Idempotent Mar 14 '15 at 14:18
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Possible duplicate of Stochastic calculus book recommendation – May 18 '18 at 22:22
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2Does this answer your question? Where to begin in approaching Stochastic Calculus? – user95921 Dec 28 '23 at 01:37
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I like the book Brownian Motion - An Introduction to Stochastic Processes by René Schilling and Lothar Partzsch pretty much:
- As the title of the book suggests, it concentrates on Brownian motion which is, without any doubt, the most famous and most important stochastic process (with continuous sample paths). It discusses path properties of Brownian motion, presents several ways how to construct Brownian motion and introduces stochastic integrals with respect to Brownian motion. Moreover, it contains two chapters on stochastic differential equations as well as a chapter on the connection to PDEs.
- The book starts right from basic definitions and properties; the reader should be familiar with measure/probability theory and the basics of (discrete) martingale theory.
- There are full solutions to all exercises available on the web.
- The book is rigorous (in contrast to the book by Oksendal which has already been mentioned in a comment).
saz
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Oksendal is a classic. I personally really liked Klebaner-Stochastic Calculus with Applications. It was really well written and insightful. Somewhat rigorous, but still intuitive.
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Thank you! Great to have a variety of recommendations! It's both for a student and for my own edification, so we will likely use more than one! – Idempotent Mar 14 '15 at 14:20