Stochastic Integration Theory (Oxford Graduate Texts in Mathematics Book 14) 1st Edition by Peter Medvegyev (PDF)

Description

This graduate level text covers the theory of stochastic integration, an important area of Mathematics that has a wide range of applications, including financial mathematics and signal processing. Aimed at graduate students in Mathematics, Statistics, Probability, Mathematical Finance, and Economics, the book not only covers the theory of the stochastic integral in great depth but also presents the associated theory (martingales, Levy processes) and importantexamples (Brownian motion, Poisson process).

User’s Reviews

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

⭐I am a PhD student studying econometrics who needed to learn semimartingale theory for my dissertation. This book does an excellent job introducing the field while going into sufficient detail to make an more in depth book unnecessary. I’ve learned more from this book than from few other books that I have used. I still find my self referencing it frequently. It is a PhD level math book, and so it cannot be simple.

⭐This a good book on stochastic integration.The author is completely honest with the reader in the whole book specially in the preface where he shares his suffering when trying to understand the subject. You can expect then a text composed by someone who is worried about the details and understanding. As an exampleyou can find insights about the intuitive idea behind the concept of progressive measurability. I think that no other text tries to do that.The book treats stochastic integration in a general setting but it does not leave the Brownian case aside. There are a lot of examples about it sprinkled throughout the book. There are no exercises in the book but this is not a problem. If you like solving exercises close the bookjust before the proof of a theorem or try to develop the examples by yourself (most of the examples are stated just like exercises).I found particularly interesting the construction of the stochastic integral in the case of locally square-integrable martingales. The authordevelops what he calls an Itô-Stieltjes integral and uses this tool to prove the existence of the quadratic variation process. Other booksintroduce quadratic variation first. I like Medvegyev’s approach better since is more intuitive.The book is very comprehensive and I recommend you to take a lookvia amazon look inside feature.The author maintains a website with an errata an some improvements.

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