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1. Elementary probability theory.

2. Poisson processes.

3. The Markov property.

4. Stochastic processes.

5. Realise that you’re missing a background in analysis, therefore you don’t know sh?t about measure theory but you actually need it to know anything deeper . Wonder to yourself if you really want to spend the next 3 years getting a maths background you don’t have.

6. Convince yourself that it’s all just engineering and middle through by picking a project involving non trivial markov chain.

7. Go back and spend 3 years doing foundational maths then repeat point 1-5.

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While I agree with the progression of knowledge listed here I don't think it requires 3 years of foundation to math. If you have a basic understanding of math already you should be able to pick up the theory fairly well in a couple of months of research and application.

I think when you get out of the basic linear algebra and calculus prerequisite and into the analysis and measure theory prerequisite nothing takes a few months anymore :)

You don't need much math to pick up the very basic theory, but after a certain point you're going to hit a hard wall unless you have a strong background in analysis.

Poisson processes are continuous time though. If you're interested in Markov chains you only need the discrete-time theory.

In discrete time and discrete space, it mostly just reduces to linear algebra.

No, can do continuous time discrete state space theory -- the jumps in the discrete state space are at the arrival times of the Poisson process -- that works out easily enough, especially if using Monte-Carlo. See my other post here on Red/Blue stuff.

Unless you’re interested in continuous markov chains, infinite state spaces, renewal theory, excessive functions, and so on.

That whole math sequence was part of my MBA program that culminated in Markov chains for synthetic options pricing after like, 9 months. And this is for business school students; not engineers :)

Sure, and for any given application it’ll be possible to explain Markov chains as they apply to it. I recently did a financial valuation course where we did an “intuitive derivation of Itos formula” so that we could skip the measure theory prerequisites. We also skipped talking about Reimann integrals and just accepted that sums are integrals at a limit ... we also glossed the separating hyperplane theorem so that we could say “no arb iff risk neutral measure exists”, and so on.

However, if you actually want a background in the theory of Markov chains, I don’t think this approach works.

Just work with discrete state spaces and otherwise be less concerned with measure theory. E.g., in stochastic control problems, don't sweat measurable selection!

Can you recommend textbook on these topic?

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