I am looking for the book about advanced stochastic process.

It may cover the following content:

  1. Stochastic matrices. Ex: $A(k)$, where $k$ is the time index.
  2. Stochastic process in space (not just in time).
  3. Contents from real analysis (Ex: application of monotone convergence theorem, Fatou' Lemma, increasing sequence of random variables).
  4. Miscellaneous topics (such as supermartingale convergence theorem, or convex function discusstion).

I am not sure my description is accurate or not, but I will fix it if possible.

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    $\begingroup$ I don't think you'll find one book that does this. For example, #3 is normally covered in books for a first course like Williams' Probability with Maringales, Durrett's Probability: Theory & Examples or more advanced intro books like Billingsley's Probability & Measure/Dudley's Real Analysis and Probability/Pollard's User's Guide to Measure Theoretic Probability. The rest of the topics normally are best treated by books on the particular topic. $\endgroup$ – Batman Dec 25 '15 at 3:23
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    $\begingroup$ Thanks, my background is from EE. So we usually use the textbook without much theoretical contents. And my interest now is in convex optimization over random networks. Many papers require such background. And I just finish the course of real analysis in graduate level $\endgroup$ – sleeve chen Dec 25 '15 at 3:43
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    $\begingroup$ Maybe the Dudley's one is closer. $\endgroup$ – sleeve chen Dec 25 '15 at 3:57

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