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# Questions tagged [stochastic-matrices]

A stochastic matrix (also termed probability matrix, transition matrix, substitution matrix, or Markov matrix) is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability.

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### Comparison of time until absorption for two absorbing Markov chains

Let $\{X_t, t \geq 0\}$ and $\{X_t', t \geq 0\}$ denote two markov chains on the same state space $\{1, ..., n+1\}$ with transition probability matrices $P$ and $P'$ respectively. Suppose that both ...
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### Ito lemma for SDEs on a Lie group

I'm trying to generalize the theorem described in this paper https://arxiv.org/abs/2001.01098 to the case of a semisimple compact matrix Lie group. In doing so i'm trying to define a formula ...
1 vote
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### Compressing covariance matrix from 3X3 to 2X2

thanks for answering my question. My question is, Let $v_3=[a,b,c]^T$ is a probabilistic 3-D vector variable which is distributed by zero mean Gaussian of dense covariance matrix $\Sigma_{3\times3}$. ...
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### On permanent of a square of a doubly stochastic matrix

Let $A = (a_{i,j})$ be a double stochastic matrix with positive entries. That is, all entries are positive real numbers, and each row and column sums to one. A permanent of a matrix $A = (a_{i,j})$ is ...
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### How to generate constant row and column sum matrices?

How can we randomly generate matrix $A \in \mathbb{R}^{n \times m}_{\geq 0}$ that satisfies $A 1_n = m1$ and $A^T 1_m = n1$.
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### Pagerank Markov chain reductions

In short: if a Markov chain models a (generalized) pagerank, is it always possible to remove any of its state and obtain a Markov chain that models a pagerank close to the initial one? Full details. ...
1 vote
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### The minimal norm of a shifted stochastic matrix

Given a row-stochastic matrix $M$ with singular values $\sigma_{1} \geq \cdots \geq \sigma_{n}$, I am looking for an upper bound on the expression \min_{\alpha} \left\| M- \frac{\alpha}{n}J_{n} \...
Are there constructive examples of doubly stochastic matrices (whose rows and columns all sum up to $1$ and contain only non-negative entries) that are not diagonalizable?
A matrix $A$ is called doubly stochastic if its entries are nonnegative, and if all of its rows and columns add up to $1$. A subset of doubly stochastic matrices is the set of pairwise averaging ...