# Tagged Questions

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### recurrent states in markov chain with poisson-like transition matrix

I am considering a Markov chain $X$ with state space $\mathbb{N}$ that has transition probabilities $p_{ij}=\begin{cases}1\mbox{ for }i=j=0\\e^{-i}\frac{i^{j}}{j!} \mbox{ otherwise }\end{cases}.$ I ...
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### Expected value of a stochastic harmonic series

It doesn't seem straightforward to put this into mathematical notation, but I'll do my best to explain the setup. Consider a harmonic series of the following type. For the sake of argument, say we ...
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### A Coupled Random Walk on the xy-Plane

Consider a point on the $xy$-plane whose position is updated in iterations. In each iteration, the point undergoes, with equal probability, either an $A$- or a $B$-update, defined as follows: ...
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### Finding Probability Generating function for $P\left\{ X > n+1\right\}$

I am trying to find probability generating function for $P\left\{ X > n+1\right\}$. Let X be a random variable assuming the values $0, 1, 2, ...$. The notation both for the distribution of $X$ ...
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### MA process ACF proof - don't understand it

I've got the proof but I don't understand a small detail. As you know for an MA process: $X_n = \sum _{i=0} ^q \beta_i Z_{n-i}$ where $Z_n$ is WGN (pure Gaussian random process). Then the ACF is: ...
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### Convergence of $\frac{a_n}{n}$ where $a_0=1$ and $a_n=a_{\frac{n}{2}}+a_{\frac{n}{3}}+a_{\frac{n}{6}}$

Given $a_0=1$ and:$$a_n=a_{\frac{n}{2}}+a_{\frac{n}{3}}+a_{\frac{n}{6}}$$Find convergence or divergence of $\frac{a_n}{n}$. Such a weird problem; I don't know how to attack it. I'm also fairly ...
$y_{MA}$ = $ε_t$ + $ε_{t-1}$ <- stationary $y_{AR}$ = $ε_t$ + $y_{AR_{t-1}}$ $y_{AR_{t-1}}$ = $ε_t$ + $ε_{t-1}$ + $y_{AR_{t-2}}$ $y_{AR_{t-2}}$ = $ε_t$ + $ε_{t-1}$ + $ε_{t-2}$ + ...