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On wikipedia there are some results on Itô's lemma applied to non-continuous semimartingales (sometimes called Itô-Doeblin lemma)

I have looked up the books by Malliaris, Oksendal and Doob, but they only mention the case of Poisson jumps, not the more general case.

Where can I find a reference and a demonstration of Itô's lemma for non-continuous semimartingales?

gypsophila
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    Well, books on jump processes, right? E.g. the book by Ikeda & Watanabe or Protter or Jacod & Shiryaev or.. – saz Sep 20 '18 at 05:08

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As saz pointed out, there are several books on jump processes which give demonstrations and examples on semimartingales. Some of these books are:

  1. Stochastic Differential Equations and Diffusion Processes - Ikeda & Watanabe
  2. Stochastic Integration and Differential Equations - Philip E. Protter
  3. Limit Theorems for Stochastic Processes - Jacod & Shiryaev
  4. Introduction to stochastic calculus with applications - Fima C. Klebaner
gypsophila
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