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Results tagged with markov-chains
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user 20062
1
vote
1
answer
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Empirical distribution of a collection of iid Markov chains
Suppose we have $N$ independent 2-point Markov chains each having a rate matrix $Q = [-1,1;1,-1]$ and stationary distribution $\pi = [0.5,0.5]$. At time $t=0$, we initiate the chains so that the empir …
- 1,034
4
votes
Accepted
Convergence of Markov chains in terms of relative entropy
Turns out $D(p_t||\pi)$ need not always be convex. The following paper demonstrates a counter-example in section $4.2$- http://arxiv.org/abs/0712.2578
- 1,034
6
votes
1
answer
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Convergence of Markov chains in terms of relative entropy
Consider a finite state, irreducible Markov chain with a rate matrix $Q$ and a stationary distribution $\pi$. Suppose the chain starts with the initial distribution $p$ at time $0$, then at time $t$ t …
- 1,034