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（‘transposing?state?valuation?vector‘）;
????V=V‘;??%?change?it?to?a?column?vector
??else;
????return;
??end;??
end
if?s0??r;
??disp（[‘initial?state?‘num2str（s0）‘?is?out?of?range‘]）;
??disp（[‘initial?state?defaulting?to?1‘]）;
??s0=1;
end;

%?The?simulation?of?Markov?chain?formally?starts?from?here
%T
%rand（‘uniform‘）;

X=rand（n-11）;??%?generate?（n-1）?random?numbers?drawn?from?uniform?distribution?on?[01]?each?number?to?be?used?in?one?simulation.

s=zeros（r1）;???%?initiate?the?state?vector?“s“?to?be?a?rx1?zero?vector

s（s0）=1;????????%?change?the?“s0“th?element?of?“s“?to?1

cum=T*triu（ones（size（T）））;?
%?“triu（ones（size（T）））“?generates?an?upper?triangular?matrix?with?all?elements?equal?to?1
%?cum?is?a?rxr?matrix?whose?ith?column?is?the?cumulative?sum?from?the?1st?column?to?the?ith?column?
%?the?ith?row?of?cum?is?the?cumulative?distribution?for?the?next?period?given?the?current?state.?

for?k=1:length（X）;??%?“l(fā)ength（X）“?returns?the?size?of?the?longest?dimension?of?X.?“k“?indicates?the?kth?simulation.?
????
??state（:k）=s;?????%?state?is?a?matrix?recording?the?number?of?the?realized?state?at?time?k?
??
??ppi=[0?s‘*cum];???%?this?is?the?conditional?cumulative?distribution?for?the?next?period?given?the?current?state?s
??
??s=（（X（k）<=ppi（2:r+1））.*（X（k）>ppi（1:r）））‘;????
??%?compares?each?element?of?ppi（2:r+1）?or?ppi（1:r）?with?a?scalar?X（k）?and
??%?returns?1?if?the?inequality?holds?and?0?otherwise
??%?this?formula?assigns?1?when?both?inequalities?hold?a

?屬性????????????大小?????日期????時(shí)間???名稱
-----------?---------??----------?-----??----
?????文件??????684032??2009-11-27?10:55??馬爾科夫鏈\Markov.ppt
?????文件????????3040??2018-04-26?09:38??馬爾科夫鏈\markov.m
?????文件?????2048000??2009-11-27?10:58??馬爾科夫鏈\馬爾可夫鏈預(yù)測(cè).ppt
?????目錄???????????0??2018-05-08?10:04??馬爾科夫鏈\