Arsthbt

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
usetikzlibraryautomata,chains
begindocument
begintikzpicture[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.
endtikzpicture
enddocument

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
usetikzlibraryautomata,chains
begindocument
begintikzpicture[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.
endtikzpicture
enddocument