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I was looking for a good book that explains at beginner-level the basic of stochastic calculus, probability and random variables, Itô and jump processes as well as Brownian Motion.

At university we are going really fast hence I need a book to go through the basics again.

Thanks a lot.

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  • $\begingroup$ Hi there, "jump, ito, brown" ... wouldn't you like to improve the title a bit? Are you interested in "jump processes" (e.g. Lévy-processes) or jump-diffusions? Brownian motion or Ito calculus? $\endgroup$ – Ric Feb 20 at 13:14
  • $\begingroup$ Shreve is good for the less technically inclined reader (but more than what is required for hull eg). Then willmott then oksendal i would say $\endgroup$ – Ezy Feb 21 at 4:13
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The book Stochastic calculus for finance by Steven Shreve gives a good introduction to stochastic calculus applied to finance. A whole chapter is dedicated to the Itô Integral for example. It covers a large spectrum ranging from probability theory to stochastic financial models. I strongly recommend it!

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Elementary Stochastic Calculus by Thomas Mikosch is an excellent introduction to the topic in a very compact way. Alternatively, Stochastic Calculus for Finance II: Continuous-Time Models by Steven Shreve is a more comprehensive reference which is very much oriented to applications in finance.

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Consider “Paul Wilmott Introduces Quantitative Finance” if you look for an enjoyable read, good intuition and a not too academic approach

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If you're interested in learning about stochastic calculus outside of the context of quant finance (which I think is a better approach than learning about it solely in the context of finance), check out Stochastic Integration and Differential Equations by Protter.

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