Tagged Questions
0
votes
1answer
47 views
Markov Chain - Snakes and Ladders
A simple game of snakes and ladders is played on a board of nine squares. At each turn a player tosses a fair coin and advances one or two places according to whether the coin lands heads or tails. If ...
1
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0answers
19 views
Estimate on Galton-Watson process distribution
Let $(Zn)_{n\in \mathbb N_0}$ be a Galton-Watson process, i.e.
$$ Z_{n+1} = \sum_{k=1}^{Z_n}\xi_{n,k},\qquad (\xi_{n,k})_{n\in \mathbb N_0,k \in \mathbb N} \quad \text{i.i.d } \mathbb N_0 \text{ ...
-1
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1answer
70 views
Markov Chain Stationary distribution
I constructed a 4*4 state transition matrix from a discrete-time Markov Chain Model as follows:
A=[p0 p0 p0 p0;
p*p0+(1-p) p0 p0 p0;
p0 p*p0+(1-p) p0 p0;
p0 p0 p*p0+(1-p) ...
0
votes
1answer
49 views
Stationary Distribution of T
I'm trying to find the stationary distribution of T, a transition matrix (Markov Chain). After I solve the equations of the matrix, I can't get to their values, does that mean that T doesn't have a ...
0
votes
0answers
75 views
Reversibility of Markov Process and Exponential Distribution of Transition Rates
I am reading the paper Towards Utility-optimal Random Access Without Message
Passing by J. Liu, Y. Yi, A. Proutiere, M. Chiang, H. V. Poor. A sentence in Section 3.2 can be paraphrased as follows:
...
1
vote
1answer
58 views
Why does this probability equivalence of events hold?
$P(X_0 = j, X_m \ne j, 1 \le m \le n-1) = P(X_m \ne j, 1 \le m \le n-1) - P(X_m \ne j, 0 \le m \le n-1) $
Where
$\{X_n\}$ is an irreducible Markov Chain with a finite state space.
3
votes
1answer
536 views
coin flips and markov chain
Consider the case of an infinite (or finite $n$) string of coin tosses, and let $q$ and $1-q$ be the probabilities that the coin comes up tails and heads, respectively. (For simplicity, we can take ...
