| Schritte |
Prozessmatrix |
| $0$ |
$P^0 = \begin{pmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{pmatrix}$
|
| $\dots$ |
|
| $n$ |
$P^{n} = \begin{pmatrix}
0.8 & 0.1 & 0.3 \\
0.1 & 0.7 & 0.1 \\
0.1 & 0.2 & 0.6
\end{pmatrix} \cdot P^{n-1}$
|
| $\dots$ |
|
| $\downarrow$ |
|
| $\infty$ |
$P_{\infty} = \begin{pmatrix}
0.5 & 0.5 & 0.5 \\
0.25 & 0.25 & 0.25 \\
0.25 & 0.25 & 0.25
\end{pmatrix}$
|
|
| Schritte |
relative Verteilungsvektoren |
| $0$ |
$\vec{v}_{0} = \begin{pmatrix}
a \\
b \\
c
\end{pmatrix}\quad$ mit $a+b+c = 1$$
|
| $\dots$ |
|
| $n$ |
$\vec{v}_{n} = P^n \cdot \vec{v}_{0}$
|
| $\dots$ |
|
| $\downarrow$ |
|
| $\infty$ |
$\vec{v}_{\infty} = P_{\infty} \cdot \vec{v}_{0} =
\begin{pmatrix}
0.5 \\
0.25 \\
0.25
\end{pmatrix}$
|
|
