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# Questions tagged [markov-chains]

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### Distribution of markov chain with a stopping time

I have a Markov chain $X_0, X_1, ..., X_\tau$, where $X_0$ is sampled from the stationary distribution and $\tau$ is a stopping time. Is it true that for any fixed $k$, $X_k$, given that $k \leq \tau$,...
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204 views
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### Why do we assume that $\mathcal{A}$ is an algebra in this 2003 paper of Bobkov and Tetali?

In the following paper (extended version here), at the beginning of section 3, the authors give two axioms about $\mathcal{A}$. Axiom 1 is about $\mathcal{A}$ being an algebra. I do not see where this ...
0answers
53 views

### Convexity of conditional relative entropy for Markov distributions

Consider two Markov processes $p$ and $q$. The conditional relative entropy between them is \begin{align} D(p\parallel q)& =\sum_a p(a)\sum_b p(b\mid a)\log\frac{p(b\mid a)}{q(b\mid a)}\\ & =\...
1answer
147 views

### Markov chain and random iteration of functions

Could anyone give me some references for the convergence rate( assuming having a stationary distribution) of such Markov chain arising from the random iteration of a FINITE number of Lipschitz ...
0answers
187 views

### Maximize an $L^p$-functional subject to a set of constraints

Let $(E,\mathcal E,\lambda)$ and $(E',\mathcal E',\lambda')$ be measure spaces $f\in L^2(\lambda)$ $I$ be a finite nonempty set $\varphi_i:E'\to E$ be bijective $(\mathcal E',\mathcal E)$-measurable ...
1answer
159 views

### Existence and uniqueness of a stationary measure

This same question was also posted on MSE https://math.stackexchange.com/questions/3327007/existence-and-uniqueness-of-a-stationary-measure. Recently I have posted the following question on MO ...
0answers
88 views

### Characterizing the relationship between element-wise Markov transitions and the full-conditionals of the stationary distribution

Consider a $p$ dimensional random variable with a discrete support. Consider a Markov transition kernel on the state space that is defined in terms of element-wise transition distributions. One can ...
1answer
107 views

0answers
69 views

### Distribution of a linear pure-birth process' integral

I stumbled across the following random variable, defined as the integral of a linear pure-birth process i.e. a Yule process: $$Z_t = \mathbb{E}\bigg[\int_0^t Y_s ds \bigg| Y_t=k , Y_0=1\bigg]$$ ...
0answers
17 views

### Simulating an inhomogeneous DTMC with transition matrix dependent on Xn

I am simulating an agent navigating through space, where the agent's navigation strategy changes over time as a Markov chain with transition probabilities dependent on its position in space. ...
2answers
223 views

### Slowest initial state for convergence of finite birth-and-death Markov chains

Consider the continuous-time birth-and-death Markov chain on $\{1,\cdots,n\}$ with all rates equal to $1$. Is it true that the convergence to equilibrium, in total variation distance, is slowest when ...
1answer
84 views

### Reference request: When is the variance in the central limit theorem for Markov chains positive?

I'm looking for a reference which gives sufficient conditions for the variance to be positive in the central limit theorem for Markov chains (cf https://en.wikipedia.org/wiki/...

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