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Results tagged with markov-chains
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user 1131
2
votes
Accepted
Total offspring of Poisson multitype branching process
Yes, with essentially the same proof. In the scalar case, just notice that $e^{cX_n+bZ_n}$ is a supermartingale as long as $p(e^{c+b}-1)\le b$. In the vector case you will need to find positive vector …
- 61.9k
11
votes
Accepted
An interesting Markov chain with uniform marginals
Since I was requested to elaborate, here goes. First, let's look at the automorphism of the unit circle induced by this mapping (written in the least revealing way). With $z=e^{it}$, as usual, we have …
- 61.9k
10
votes
Accepted
Bounds on $\|P^{k+1} - P^k\|$ for $n$ by $n$ stochastic matrix $P$ with trace $n-1$ and inte...
OK, I think I have a full answer at this point, so let me post it.
Step 1. (algebra).
If $P$ is an $n\times n$ stochastic matrix and $\lambda$ is an eigenvalue of $P$ with $|\lambda|=1$, then $\ …
- 61.9k
3
votes
Accepted
"Induced" arrivals in an M/M/1 queue?
Just introduce extra states. The total description of a state will include the length of the queue and the stage of service for the current customer. For instance, if each initial service may result i …
- 61.9k