Distribution stationnaire d'une chaine de MarkovLe but est de calculer la distribution stationnaire d'une chaine de Markov en temps discret. On se donne la matrice de transition sous forme numerique ou symbolique.

restart;with(linalg);

Warning, the protected names norm and trace have been redefined and unprotected

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Fonctions utilis\351es: rowdim coldim diag transpose kernel ERROR nops op add map normaldistr_stationnaire := proc (P::matrix) local N, Id, m, n, P1, pi, somme; n := rowdim(P); m := coldim(P); if m <> n then ERROR("dimensions incorrectes") end if; Id := diag(1$n); P1 := transpose(Id-P); N := kernel(P1); if nops(N) <> 1 then ERROR("Noyau incorrect") else pi := op(kernel(P1)) end if; somme := add(pi[i],i = 1 .. n); map(normal,evalm(pi/somme)) end proc:

P := matrix([[1-a, a], [b, 1-b]]);

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pi := distr_stationnaire(P);

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A faire