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I would like to get a good feeling of stochastic integration in a more intuitive way (to be able to easily explain it to a first year math student or a physicist). Example of what I want to understand better:

  1. Which processes we can put as integrators, integrands when we calculate stochastic integrals, what are the limitations, etc?
  2. What was the history of development of stochastic integration? ( I know that key people are Meyer, Itō, but maybe somebody occasionally found nice article about the path of development of the discipline).

I have seen several posts, one of it is full of references to nice books, here is a link: What are some easier books for studying martingale?

My recommendation of books to read: I really liked the prefrace given by P. Medvegyev, Stochastic Integration Theory ( did not see anyone mentioning this book here) and of course the way the material is treated at famous Rogers, Williams, Diffusions Markov Processes and Martingales has some storytelling magic. It is not as dry as other books can be. I like the dependence charts people put in the books, like R.Schilling did in Measures, Integrals and Martingales.

To sum up, do you know any good overview, or guide or a book that deals with theory providing a concise story, that glues the material together. Sorry if I ask something inappropriate or I am repeating many posts here.

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  • $\begingroup$ A first year undergraduate? $\endgroup$ – Batman Mar 5 '17 at 22:41
  • $\begingroup$ me? almost surely ) $\endgroup$ – StochasticIntegrationStudent Mar 5 '17 at 22:49
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Update on subquestion 2: a friend advised to read history of the discipline in this paper: A short history of stochastic integration and mathematical finance: the early years, 1880–1970

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I find Martingales and stochastic integration by P.E. Kopp a nice introduction as well.

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