Htydjtk

I am trying to create something similar to using this example. I modified the source code and this is what I have

documentclass[tikz]{standalone}

usetikzlibrary{automata,chains}

begin{document}

begin{tikzpicture}[start chain=going left,node distance=2cm]   

node[state, on chain]                 (N+1) {N+1};

node[state, on chain]                 (N) {N};

node[on chain]                   (g) {...};

node[state, on chain]                 (2) {2};

node[state, on chain]                 (1) {1};

node[state, on chain]                 (0) {0};

draw[

    >=latex,

%   every node/.style={above,midway},% either

    auto=right,                      % or

    loop above/.style={out=75,in=105,loop},

    every loop,

    ]

     (0)   edge[loop above] node {$p_{0,0}$}   (0)

           edge             node {$p_{0,1}$} (1)

     (1)   edge[loop above] node {$p_{1,1}$}   (1)

     (1)   edge             node {$p_{1,2}$}   (2)

     (2)   edge[loop above] node {$p_{2,2}$}   (2)

           edge             node {$p_{2,3}$}   (g)

     (g)  edge node {$p_{N-1,N}$}   (N);

     (N)   edge[loop above] node {$p_{N,N}$}   (N)

     edge             node {$p_{N,N+1}$}   (N+1)

     (N)   edge[bend left] node {$p_{N,N}$}   (0)

     (N+1)   edge[loop above] node {$p_{N+1,N+1}$}   (N)         

     (N+1)   edge[bend left] node {$p_{N+1,N+1}$}   (0)

        % The draw path is like the one above.

end{tikzpicture}

end{document}

However, I seem not to get it right. Where did I get this wrong?

You were almost there. You only misplaced the semicolon and confused a label.

documentclass[tikz]{standalone}

usetikzlibrary{automata,chains}

begin{document}

begin{tikzpicture}[start chain=going left,node distance=2cm]   

node[state, on chain]                 (N+1) {$N+1$};

node[state, on chain]                 (N) {$N$};

node[on chain]                   (g) {$cdots$};

node[state, on chain]                 (2) {$2$};

node[state, on chain]                 (1) {$1$};

node[state, on chain]                 (0) {$0$};

draw[

    >=latex,

%   every node/.style={above,midway},% either

    auto=right,                      % or

    loop above/.style={out=75,in=105,loop},

    every loop,

    ]

     (0)   edge[loop above] node {$p_{0,0}$}   (0)

           edge             node {$p_{0,1}$} (1)

     (1)   edge[loop above] node {$p_{1,1}$}   (1)

     (1)   edge             node {$p_{1,2}$}   (2)

     (2)   edge[loop above] node {$p_{2,2}$}   (2)

           edge             node {$p_{2,3}$}   (g)

     (g)  edge node {$p_{N-1,N}$}   (N)

     (N)   edge[loop above] node {$p_{N,N}$}   (N)

     edge             node {$p_{N,N+1}$}   (N+1)

      (N)   edge[bend left] node[below] {$p_{N,N}$}   (0)

     (N+1)   edge[loop above] node {$p_{N+1,N+1}$}   (N)

      (N+1)   edge[bend left] node[below] {$p_{N+1,N+1}$}   (1);

%         % The draw path is like the one above.

end{tikzpicture}

end{document}