Feb 17, 2026 · 4 That "Fundamental Theorem of Markov Chains" is an application of the Perron-Frobenius Theorem from linear algebra; see this subheading of that Wikipedia link. There is an …

Feb 24, 2026 · I am analyzing a discrete-time Markov chain that can grow exponentially but also suffers from frequent, severe drops. I want to find the exact probability that it reaches a certain threshold …

I would like to know what books people currently like in Markov Chains (with syllabus comprising discrete MC, stationary distributions, etc.), that contain many good exercises. Some such book on

Now in markov chain a steady state vector ( when effect multiplying or any kind of linear transformation on prob state matrix yield same vector) : qp=q where p is prob state transition matrix this means Y = …

Mar 24, 2024 · I have seen in two places, different requirements for a Markov chain to converge to its stationary/invariant distribution: Irreducibility and aperiodicity. As mentioned here Irreducibility and

Aug 14, 2016 · My question is a bit more basic, can the difference between the strong Markov property and the ordinary Markov property be intuited by saying: "the Markov property implies that a Markov …

Apr 28, 2022 · 0 Imagine the following Markov chain: $$\begin {bmatrix} 0 & 0.5 & 0.5 \\ 1 & 0 & 0 \\ 1 & 0 & 0\end {bmatrix}$$ We always get back to state 1 in two time periods. So, state 1 is periodic and …

Nov 27, 2024 · Yes, this is a version of the Chapman-Kolmogorov equation. Let $ (Z_0, Z_1, Z_2)$ be a Markov chain taking values in some finite or countable space.

Sep 9, 2021 · As a Markov chain, it seems that the states represent the possible discrepancy between heads and tails. You start with 1 extra tails. Each time you flip the coin, a heads moves you to a state …

The first definition is preferable. Ergodic Markov Chain is also called communicating Markov chain is one all of whose states form a single ergodic set; or equivalently, a chain in which it is possible to go from …