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I am studying Durrett's Advanced Probability Theory, 5th ed. However, I find it very helpful to have more intuitive explanations like this.

May I ask if there a textbook or online course or online video or any other resources like this?

RobPratt
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dodo
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    +1 : to your posting for asking, what is in my opinion, a very worthwhile question. Further, this forum is, in my opinion, the very best place to ask the question. Personally, I don't know the answer. – user2661923 Nov 17 '23 at 21:26
  • I doubt any book will spend time on explaining something like this. The difference between strong Markov and Markov property is pretty obvious. On the other hand, durrett’s other book Martingales in analysis is very well written. – Andrew Nov 17 '23 at 21:29
  • Durret's book does cover this in the chapter on Markov Chains. – Mason Nov 18 '23 at 01:51
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    Regarding the intuitive difference between Markov and strong Markov property: imho this is probably as intuitive as the difference between functions being differentiable but not continuously differentiable. The correct comment in your linked post that any discrete Markov chain is automatically strong Markov indicates that the strong Markov property is a technical condition of continuous Markov processes that is generally violated only by more or less pathological examples. Advice: try to understand the intuition behind the simple Markov property and move on. – Kurt G. Nov 18 '23 at 05:14
  • Karatzas & Shreve write in the notes to ch. 2 of their book Brownian Motion and Stochastic Calculus that "It seems rather amazing today that a complete and rigorous statement about the strongly Markovian character of Brownian motion (Theorem 6.16) was proved only in 1956; see Hunt (1956)." Intuition about strong vs simple MP? Go away! – Kurt G. Nov 18 '23 at 18:03

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