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Last semester I attended a course about stochastic calculus. There we constructed the stochastic integral with respect to continuous semimartingales. We restrict ourselves to the continuous case. However there is a general theory about semimartingales, which I want to study. I'm interested in mathematical Finance, where we often study not continuous processes. This semester I attend a course, where use some result from the general theory without really knowing the basis, which is not satisfyingly (at least for me). Therefore I want to study this general theory in a more rigorous way. My question is therefore, which books are recommended to study this theory. Of course the most famous book is Doob-Meyer. I found also the book "General semimartingale theory and stochastic calculus" by Sheng-Wu He, Chia-kang Wang, Jia-An Yan". Does someone know this book and could recommend it? I worked through the first pages and really like the style. I also worked through some pages of Doob-Meyer, but it seems for me to comprehensive to start with. It would be really appreciated if someone could share his or her experience. I am thankful for any advice.



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The book Stochastic Processes by Richard F. Bass seems helpful for your case. Chapter 16 of this book deals with the general theory of processes, and I think this is one of the most comprehensive introduction to the general theory of stochastic calculus, including the celebrated Doob-Meyer decomposition. It also covers various topics in a tangible manner. One disadvantage of this book is that its exercises are not elaborated and sometimes go beyond the scope of the chapter where they belong to. – Sangchul Lee Nov 5 '12 at 13:22
@ Math : You also have Protter's Book but often the redaction of the proofs are sometimes a little hasty in my opinion. Otherwise you have the wonderful blog of George Lowther "Almost Sure" which is really nice and comprehensive on stocastic integration with respect to semi-martingales, even if it has an original approach to the theory it is really incredibly pedagogical.Best regards – TheBridge Nov 5 '12 at 13:31
@TheBridge : I do not really like Protter's book. I know George Lowther blog, and I will for sure have a look at it. But somehow I like more to work with a book with exercises instead of a blog. – math Nov 5 '12 at 13:54
@sos440 Thanks for you suggestions! This was also a book on my "list". I will have a look at it. – math Nov 5 '12 at 13:55
You may also try the book "Stochastic integration with jumps" by K. Bichteler. It has a lot of exercises. A version of the book is available on authors' homepage.. – Julian Wergieluk Nov 6 '12 at 16:56

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