latex State Transition Diagram of a Markov Chain


Suppose the following matrix is the transition probability matrix associated with a Markov chain.

    0.5   0.2  0.3
P=  0.0   0.1  0.9
    0.0   0.0  1.0

In order to study the nature of the states of a Markov chain, a state transition diagram of the Markov chain is drawn.

\begin{tikzpicture}[->,>=stealth',shorten >=2pt, line width=3pt, 
                                  node distance=2cm, style ={minimum size=20mm}]
\tikzstyle{every node}=[font=\huge]
\node [circle, draw] (a) {1};
\path  (a) edge [loop above] (a);
\node [circle, draw] (b) [right=of a] {2};
\path  (b) edge [loop above] (b);
\draw[->] (a) -- (b);
\node [circle, draw] (c) [below=of a] {3};
\path  (c) edge [loop below] (c);
\draw[->] (a) -- (c);
\draw[->] (b) -- (c);

enter image description here