Questions tagged [transition-matrix]

Question 1

I have a matrix where each row contains exactly $k$ nonzero elements, each equal to $\dfrac{1}{k}$. Therefore, the sum of each row is $1$. Each row is essentially a permutation of zeros and $k$ ...

Question 2

Let $(X,\mathcal{F})$ be a measurable space. $\nu,\mu$ are two $\sigma$-finite measure on $\Omega$ such that $\mu\ll \nu$. $P:X\times \mathcal{F}$ is a Markov kernel. One can shows $\mu P\ll \nu P$ as ...

Question 3

Let $\mathcal{S}$ be the state space, and the transition kernel to be $K_i(s,ds') = \sum_{a} P^k(ds'|s,a)\pi_{{\theta_i}}(a|s)$. How do I upper bound $\|K_1-K_2\|$. What I have tried is to follow the ...

Question 4

I am currently trying to do a spectral decomposition of this matrix $$ P = \begin{bmatrix}0&0&1\\0&1-e&e\\1-e&0&e\end{bmatrix}$$ I have eigenvalues of $1$, $1-e$ and $e-1$ with ...

Question 5

Assume a directed graph $G=(V,E)$ and that it is the graphical representation of a Markov Chain with transition matrix $P$. Then, the graph vertices stand for the Markov Chain states and edges for ...

Question 6

For the following transition probability matrix $$ P = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0.3 & 0.1 & 0.3 & 0.3 \\ 0.4 & 0.1 & 0.4 & 0....

Question 7

Let $V$ be the collection of polynomials with coefficients in $F$ in the variable $x$ of degree at most $n$. Determine the transition matrix from the basis $1,x,x^2,\ldots, x^n$ for $V$ to the ...

Question 8

Consider a Markov transition matrix $ M $ for a population distribution between two cities. Let the initial state of the system be given by: $$ u_0 = \begin{bmatrix} a - b \\ b \end{bmatrix} $$ where $...

Question 9

There is a Markov chain with states labeled by {1, 2, 3, 4, 5} and transition matrix: \begin{bmatrix} 1/2 & 1/4 & 1/4 & 0 & 0 \\ 0 & 1/2 & 1/8 & 3/8 & 0 \\ 0 & 0 &...

Question 10

There's a markov chain and transition matrix: $$ \begin{bmatrix} 1/2 & 1/4 & 1/4 & 0 & 0 \\ 0 & 1/2 & 1/8 & 3/8 & 0 \\ 0 & 0 & 0 & 3/4 & 1/4 \\ 0 & ...

Question 11

I am trying to model LFU cache operation using Markov chain. Users request contents that follow a known discrete distribution. The cache size is $n$ and there are $N$ number of contents. There are ${N ...

Question 12

I'm a bit confused with this. Since $I(X;Y) = I(Y;X)$, at first I thought it implies that Capacity($\mathbf{P}$) = Capacity($\mathbf{P}^T$), i.e., the capacity achieved with a transition matrix, ...

Question 13

Given $p_{A}, p_{B}, p_{C}$ so that $p_{A}+ p_{B}+ p_{C}= 1$, and the transition matrix equation $\begin{bmatrix} a+ m & -b & -s\\ -a & b+ d & 0\\ -m & -d & s\\ \end{bmatrix}\...

Question 14

I am having some trouble with the following problem Consider the Markov chain $(X_{n})_{n \geq 0}$ with state space $I = \{1, 2, 3, 4\}$ and transition matrix \begin{equation*} P = \begin{pmatrix} 0 &...

Question 15

Looking in Wikipedia and other sources, I've found that the stationary distribution of an M/M/$\infty$ queue is given by $$ \pi(x) = \left(\frac{\lambda}{\mu}\right)^x \frac{e^{-\lambda/\mu}}{x!} \...

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Questions tagged [transition-matrix]

Matrix with $k$ entries of $\dfrac{1}{k}$ per row (Markov chain transition matrix) — properties and eigenvalues?

Radon-Nikodym derivative along a Markov chain

Operator Norm Upper Bound via Policy Lipschitzness

Spectral decomposition of a one-step transition matrix $P$

Bipartite graph and transition matrix eigenvalue

Starting in state $1$ of a Markov chain, what is the probability of absorption at state $3$? [closed]

Find the transition matrix

Why does a $2\times2$ Markov matrix always have the eigenvector $[1, -1]$ associated with the eigenvalue that is not 1?

How to solve mean hitting time equations for a Markov chain with multiple target states?

How to calculate conditional probability for Markov chain

Model Least Frequently Used cache algorithm with Markov chain

Given a channel transition matrix ($\bf{P}$) of DMC channel, does the capacity of $\mathbf{P}$ equal to that achieved with $\mathbf{P}^T$?

How to calculate $p_{A}+ p_{B}$ quickly?

Determining for which values $\alpha$ and $\beta$ an $n$-step probability converges

Stationary distribution of $M/M/\infty$ queue

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