# Tagged Questions

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### Markov renewal process vs Markov Jump process

The venerable wikipedia for "Markov renewal process" says that: "a Markov renewal process is a random process that generalizes the notion of Markov jump processes". So what's the definition of a ...
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### Calculation of the Gallavotti-Cohen fluctuation theorem made by Lebowitz

I have a problem understanding a calculation in this paper (another form of the theorem an be found here at equation 11). For those who want to read the paper, I have difficulties with formula 2.14 in ...
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### Library chain stationary distribution

This is an exercise 1.47 from Richard Durrett's Essentials of Stochastic Processes p.85 (doi: 10.1007/978-1-4614-3615-7_1 or Google Books). On each request the ith of the $n$ possible books is the ...
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### Linear Algebra Stochastic Matrix and Markov Chains

I have a few true and false questions I need help with. Can someone please check my work? The product of two stochastic matrices is a stochastic matrix. This is false I found a counterexample. 2 ...
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### “Multivariate” Markov Chains

I am interested in estimating regime-switching VAR models to a regime setup I don't know the name of. I am hoping that someone can help me out with some references, or if there exists a name for it ...
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### period of product markov chain

Consider $Z_n := (X_n,Y_n)$ where $(X_n)_{n\in \mathbb{N}}$ and $(Y_n)_{n\in \mathbb{N}}$ are irreducible markov chains with periods $\lambda$ and $\mu$. We know that $(Z_n)_{n\in \mathbb{N}}$ is a ...
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### What is the difference between the forward and backward equations in a CTMC?

Given that the Forward equation in a CTMC (Continuous Time Markov Chain) is: $P'(t)=P_t G$, and the Backward equation is: $P'(t)=G P_t$, which equations should I use of the two depending on the case I ...
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### Transition probability in Continuous Time Markov Chain (CTMC)

I know that for a CTMC, the transition matrix $P(t)=e^{tQ}$, where $Q$ is the infinitesimal generator matrix of the irriducible CTMC. My question is how do I deal with situations or problems that ask ...
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### Under what circumstance should I use a Continuous time Markov Chain instead of a discrete time Markov Chain?

Why should I use one over the other, if I can basically reduce the small time-interval $h$ to be small enough that it simulates continuity? I guess this question is somewhat analogous to control ...
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### What is the transition matrix and stationary distribution of ${T}$

Let $T = (X_n:n \in \mathbb{N})$ denote a homogeneous Markov chain with state space $E=\lbrace 1, 2, 3\rbrace$ and $$\mathbb{P}(X_1=2\vert X_0=1) = \mathbb{P}(X_1=3\vert X_0=1)=\frac{1}{3}$$ as well ...
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### simple proof of the $L^2$ weak law for discrete-time ergodic Markov processes

Let $\{X_t\}_{t\in\mathbb{Z}}$ be a stationary and ergodic stochastic process with finite second moment. Von Neuman's ergodic theorem implies that the time average $(1/N)\sum_{j=0}^{N-1} X_j$ ...
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### Discrete Markov Transition Matrix

Well, I've been reading over the internet but I've been unable to find a straight answer. I've got a transition matrix for a Markov Discrete Chain. I've made the graph and according to my knowledge, ...
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### Random walk on one-dimensional lattice - understanding the expression $pe^{i\theta} + qe^{-i\theta}$

I've started reading the book - First Steps in Random Walks and in the very first example in Chapter 1 they talk about a random walk on a one-dimensional lattice. If we consider a particle starting ...
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### Why Gibbs sampling needn't “remixing”

I am generating $\mathbf{x}^{(1)}, \mathbf{x}^{(2)}, \dots, \mathbf{x}^{(n)}$ using Gibbs sampling methods. So I want $\mathbf{x}^{(1)}, \mathbf{x}^{(2)}, \dots, \mathbf{x}^{(n)} \sim$ some ...