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3
votes
0answers
148 views

Maximization of a total variation distance subject to another total variation distance in Markov chain

Suppose two dependent random variables $X$ and $V$ from finite alphabets $\mathcal{V}$ and $\mathcal{X}$ with known joint and marginal distributions are given. Let $P_{XV}$ and $P_X$ and $P_V$ are the ...
5
votes
2answers
202 views

Anticoncentration of the convolution of two characteristic functions

Edit: This is a question related to my other post, stated in a much more concrete way I think. I am interested in anything (ideas, references) related to the following problem: Suppose that $A ...
9
votes
1answer
611 views

Different uses of the word “ergodic”

There appear to be two definitions of the word ergodic. The dynamical systems definition says that a measure space $(X,\mathit B, \mu)$ and measure preserving transformation $T: X \mapsto X$ is ...
11
votes
4answers
489 views

Eigenvectors of a particular transition matrix

I am considering a Markov chain with $n$ states with a particularly nice structure. The transition matrix is as follows: \begin{equation}\mathbf{P}=\begin{pmatrix} 0 & 0& \dots&0 & 0 ...
4
votes
1answer
195 views

Approximating a hitting time for some state using the stationary distribution?

Provided a random walk on a bounded interval, with step probabilities, $p$ and $q$ and a stationary distribution $\pi$, how "bad" of an approximation is to assume that the hitting time for a position ...
1
vote
1answer
469 views

Hitting time probability in a Random Walk with possibility to die.

A Random Walker can move of one unit to the right with probability $p$, to the left with probability $q$ and it can jump again to the starting point with probability $r$ and die. Naturally $p+q+r=1$. ...