# Tagged Questions

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### Follow-up on solution to markov process equation

I asked a question here about solving a system related to an absorbing markov chain. I now have a variation where there are $m$ types (of student, job seeker, etc) each of which applies to ...
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### Definition of Perron-Frobenius eigenvalue

Consider a Markov chain with state space $X$ and transition prob. matrix $P=(p_{ij})$. Then a paper claims the following : Let $\theta \in X$ denote some fixed state. The Perron-Frobenius eigenvalue ...
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### Why are points from this matrix geometric sequence co-planar?

Let $M= \left[ {\begin{array}{ccc} a_{1,1} & a_{1,2} & a_{1,3} \\ a_{2,1} & a_{2,2} & a_{2,3} \\ a_{3,1} & a_{3,2} & a_{3,3} \\ \end{array} } \right]$, such ...
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### Measuring the entropy of a graph representing a transition probability matrix of a first order markov chain

There's a research project i'm currently working on which requires me to analyze various aspects of "worlds" represented by transition probability matrices, where the nodes represent objects in the ...
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### Why left multiplication when it comes to Markov chains?

When working with Markov chains and transition matrices $P$ we multiply from the left, meaning that for example $\mu^{(n)} = \mu^{(0)}P^n$ or that the stationary distribution satisfies $\pi = \pi P$. ...
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### Proving Product of Transition Matrices is again a Transition Matrix.

Let $P = [p_{ij}]$ be an $n\times n$ transition matrix for an $n$-state markov chain. How do you prove that $P^2$, or even better, that $P^n$ is again a transition matrix? My approach leaves me ...
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### Proof that the square of a stochastic matrix is stochastic

We know that the square of a stochastic matrix is also stochastic, because the two-step transition matrix of a Markov chain is necessarily stochastic. However, in there another way to independently ...
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### Combine transition and fertility matrices for youngest stage groups

I would like to ask how to combine the following information into the projection matrix. I do have data for transition (T) and fertility (F) stage matrices, so the projection matrix (A) is equal to ...
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### If $P$ is an invertible transition probability matrix, does $P^{-1}[i,j]$ have any interesting meaning?

Suppose we have a Markov chain transition probability matrix $P$ that is invertible, i.e., $P^{-1}$ exists. Question: Does there exist a meaningful interpretation of the $(i,j)$ entry in $P^{-1}$? ...
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### When random walk Markov matrix of the graph is normal?

I'm considering random walk on undirected graph $G$. At every time step, walker moves to a random neighbour, with all neighbours being equally likely. With adjacency matrix $A$ the random walk Markov ...
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### Reverse engineer transition matrix from steady state?

I had this open ended question. Is it possible to reverse engineer a transition matrix from the steady state. Is there a unique solution or could there be many? Basically given $P^{\infty}$ is there ...
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### From Q matrix to Markov Chain

We are in the setting of a continuous time MC, as defined by Liggett in his book on continuous time markov processes, on a countable state space $S$. All of his MCs are defined on the space of right ...
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### The second largest eigenvalue for Perron-Frobenius matrix

The Perron-Frobenius theorem is about the largest eigenvalue and eigenvector of a non-negative (irreducible) matrix. My question: Is there any estimation of the difference between the first and ...
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Quasi-stochastic In order not to make the title too long I used the term Quasi-Stochastic with this meaning: a quasi-stochastic matrix $Q$ is a square matrix $Q = ... 2answers 358 views ### How can I compare two Markov processes? There is a discrete-time irreductible Markov process with$r$possible states.$k$observations were performed. At each observation a state of process was determined.$T_0 = \lbrace 0,1,\dots ...
I want to estimate model transition matrix for a process (Markov chain). How much observiations of state do I need? I would prefer this as a function dependent on $n$, where $n$ is number of possible ...