Discrete time

Consider the classical Markov chain with two states :

$$\mathbf{P}= \left(\begin{tabular}{cc} \par 1-a & a \\ b & 1-b \\ \end{tabular} \right)$$

where $0<a,b<1$, and $a+b>0$.

This stochastic matrix admit as stationary distribution :

$$\pi=(\frac b {a+b},\frac a {a+b})$$

Take for example : $a=\frac 1 2$ and $b=\frac 1 3$, we obtain the transition matrix :

$$\mathbf{P}= \left(\begin{tabular}{cc} $\frac 1 2$ & $\frac 1 2$ \\ $\frac 1 3$ & $\frac 2 3$ \\ \end{tabular} \right)$$

Look three importation possibilities in PSI :

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'2states.hbf_r'.

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'2states.hbf_c'.

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'2states.marca'.

Note that it can be important to specify several decimal values to avoid numerical problems in Aliasing construction.

After precomputation, we obtain a '2states.simu' file (modulo row permutations) :