# transition-matrix's questions - Chinese 1answer

103 transition-matrix questions.

### Ergodic Markov chains and eigenvalues

I just read on wikipedia that a way to check whether a Markov chain is ergodic is to compute the eigenvalues of the transition matrix, and if those are all (except for 1) less than 1, then the chain ...

### Matrix exponential of an LTI system

Is there any direct proof to show that if eigenvalues of an LTI system are negative then the transition matrix ( or matrix exponential with respect to time) e^{At} decays to zero when t goes to ...

### 1 Is this process a Markov chain?

2 answers, 895 views markov-chains transition-matrix
Three white and three black balls are distributed in two urns in such a way that each contains three balls. We say that the system is in state i, i = 0, 1, 2, 3, if the first urn contains i white ...

### How to model a markov chain that randomly switches between two transition matrices?

Let's say I have a discrete time, time-homogeneous Markov chain $X = \{X_{1}, \dots , X_{n}\}$ with state space $S= \{1,2,3\}$ and a transition matrix: \begin{bmatrix} .4 & .3 & .3\\ .3 &...

### Identify integers $1 \leq n /leq 20$ where $p_{0,0}^{(n)} > 0$ by using a transition matrix

As the title says I have to answer the following: Identify integers $1 \leq n /leq 20$ where $p_{0,0}^{(n)} > 0$ by using a transition matrix. I know this is with the states {0,1,2,3,4,5,6,7} and ...

### How to calculate a transition kernel / function?

I m dealing with the Kalman filter and the Signal Process is given by X(n+1) = B*X(n) + C*W(n+1)with W(n) ∈ R^n is i.i.d standard normal distributed, B ...

### Conditional transition probabilites

I am confusing myself with a problem which I give below. Can someone please comment and point out my mistakes. Say I have a two state system $S_1$ and $S_2$ the probability to transition to the two ...

### 1 The Determinant of a Transition Matrix

Suppose we have a linear map $T$ whose matrix is $A$ such that $$A: V \rightarrow V$$ where $A$ is the transition matrix from the basis $v_1,v_2,...,v_n$ to the basis $w_1,w_2,...,w_n$. If the ...

### Repair chain example problem in find the limiting distribution of a Markov Chain

I am working through Durrett's book Essentials of Stochastic Processes, which is quite good. He had a problem in the first chapter on Markov processes, and I had trouble understanding how he obtained ...

### Probability of specific paths in a Markov Chain

I have a transition matrix $$\mathbf P = \begin{bmatrix}0.9 & 0.06 & 0.04 \\ 0.6 & 0.3 & 0.1\\0.7 & 0.25 & 0.05\end{bmatrix}$$ The different states are labeled A, I, O in ...

### Markov transition matrix: $\lim \limits_{n\to \infty} P^n$ and $\lim \limits_{n\to \infty} \frac1n \sum_{k=1}^n P^k$

Given the Markov transition matrix P=\left( \begin{array}{ccccccc} 0 & 0 & 1 & 0 & 0\\ 0 & 0.3 & 0 & 0 & 0.7\\ 1 & 0 & 0 & 0 & 0\\ 0.4 & 0 & ...

### Ergodic Markov Chain [closed]

Suppose there exists an ergodic Markov chain with symmetric transition probabilities. For this Markov chain, why is the stationary distribution uniform?

### transition matrix between bases

1 answers, 157 views inverse transition-matrix