function?[chainstate]=markov（Tns0V）;
%function?[chainstate]=markov（Tns0V）;
%??chain?generates?a?simulation?from?a?Markov?chain?of?dimension
%??the?size?of?T
%
%??T?is?transition?matrix
%??n?is?number?of?periods?to?simulate
%??s0?is?initial?state?（initial?probabilities）
%??V?is?the?quantity?corresponding?to?each?state
%??state?is?a?matrix?recording?the?number?of?the?realized?state?at?time?t
%
%?Original?author:?Tom?Sargent
%?Comments?added?by?Qiang?Chen


[r?c]=size（T）;???%?r?is?#?of?rows?c?is?#?of?columns?of?T
if?nargin?==?1;??%?“nargin“?refers?to?“number?of?arguments?in“.?So?only?T?is?provided?in?this?case
??V=[1:r];
??s0=1;
??n=100;
end;
if?nargin?==?2;??%?both?T?and?n?are?provided?
??V=[1:r];
??s0=1;
end;
if?nargin?==?3;??%?T?n?and?S0?are?provided
??V=[1:r];
end;
%?check?if?the?transition?matrix?T?is?square
if?r?~=?c;??
??disp（‘error?using?markov?function‘）;
??disp（‘transition?matrix?must?be?square‘）;
??return;??%?break?the?program?and?return
end;
%?check?if?each?row?of?T?sums?up?to?1
for?k=1:r;
??if?sum（T（k:））?~=?1;
???disp（‘error?using?markov?function‘）
????disp（[‘row?‘num2str（k）‘?does?not?sum?to?one‘]）;??%?“num2str“?converts?numbers?to?a?string.?
????disp（‘?it?sums?to?:‘）;?
????disp（[?sum（T（k:））?]）;?
????disp（[‘normalizing?row?‘num2str（k）‘‘]）;
????T（k:）=T（k:）/sum（T（k:））;
??end;
end;
[v1?v2]=size（V）;
if?v1?~=?1?|?v2?~=r???%?“|“?means?“or“
??disp（‘error?using?markov?function‘）;?
??disp（[‘state?value?vector?V?must?be?1?x?‘num2str（r）‘‘]）
??if?v2?==?1?&v2?==?r;
????disp（‘tr