How to Learn Stochastic Calculus From Ordinary Calculus: Stochastic Calculus - Calin Book Review
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- Опубликовано: 10 май 2022
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An Informal Introduction To Stochastic Calculus With Applications: amzn.to/42lftyR
An Informal Introduction To Stochastic Calculus With Applications 2nd Edition: amzn.to/3LWTwAk
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Book review for An Informal Introduction To Stochastic Calculus by Calin. This text teaches stochastic calculus assuming knowledge only of ordinary calculus.
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I remember taking a course in stochastic differential equations during my masters, specifically i remember being about 2/3’s in and we started with the change of measure. And I was stuck haha! Computationally it was not to bad, just finding that Girsanov kernel. But I never did quite grasp why that was needed.
That's awesome! Learning this subject the traditional way is challenging I'm sure. I'll get there sometime soon too.
This book has an entire chapter dedicated to Girsanov's theorem that I have not read. I do not see anything about a Girsanov kernel, but hopefully this excerpt from the chapter helps:
"After setting the basis in martingales, we shall prove Girsanov’s theorem, which is the main tool used in practice to eliminate drift".
Thanks for sharing!
Thank you!
You're welcome.
I covered the second edition here in a newer video:
ruclips.net/video/QN7K489RQ5I/видео.html
Thank you!
Great video thanks! Please do more on stochastic calc, content is so scarce on youtube
Please do, that would be great!
Are you familiar with the stochastic calculus book by Mikosch? His book has a quant slant but overall I think is a good intro to this superb subject
Yes I am! I don't recall if I mention it in the video, but if not then it's a shame because it is a great reference and read for anyone making this journey.
Thanks for mentioning it!
Would you say that stochastic pde is the “top” of this subject? i.e. what would immediately come after stochastic pde? Also, would you recommend the following order for eventually studying stochastic pde: baby rudin, measure/probability, stochastic processes, stochastic calculus, stochastic pde? I really like this content btw thanks!
I'll admit that there people more qualified than myself to answer your questions, but I will try my best regardless.
Honestly, I cannot give you an answer with 100% certainty. You can look into stochastic differential geometry after SDEs or SPDEs. There's a classic textbook by Ikeda and Watanabe that is very complicated and is used as a second or third book after learning stochastic calculus rigorously. There's also the text Stochastic Differential Geometry at Saint Flour.
Additionally fractional SDEs have apparently become popular in recent years. There are many books with many real life applications and modeling such as the one by Atangana and Araz.
Traditionally I would say yes. That would have been the only way to do it in the past. There are many modern books in the field of stochastic calculus that do not require such an abundance of knowledge. Such as the SPDE text by Lototsky and Rozovsky that only assume knowledge of Analysis and Probability. Thus something like Rudin and then maybe something like Rosenthal's probability would be sufficient. If you want a more complete overview of stochastic calculus then you could use Baldi before a text on SPDEs. If you are serious about wanting to do research in the field then you'll probably want to do it in the order you mentioned. So it could look something like Rudin, Axler's MIRA, Rosenthal (stochastic processes and/or Probability), Baldi, Lototsky.
For anyone else interested: this is only one route, there are many many other routes varying in degrees of difficulty, requiring many different combinations of subjects as prerequisites. I'd imagine that this route would best prepare you for research in this field though.
Hope that helps.
"top" is a vary vaguely defined idea. Subjects like rough path theory, stochastic optimal control theory, stochastic geometry (SLE), functional stochastic calc (malliavin) would be subjects to study after a thorough understanding of Stochastic Calculus (say at the level of Oskendals text).
@@JaGWiREE THANK YOU SIR! 😁