function [A,C] = markov_approx(P,m,n)
A = pnormdim(ones(m,m,n-1),1);
C = pnormdim(ones(m,1,  1),1);

for t=2:n
  prefdim = repmat([m],[1 t-1]);
  for shrt = 1:m
    pshrt = getPX(P,m,n,shrt,  t-1) + realmin;
    for Xt = 1:m
      pjshrt = getPX(P,m,n,[shrt Xt],t-1:t);
      part = pjshrt / pshrt;
      A(Xt,shrt,t-1) = part;
    end
  end
end

% compute the initial prob C
for x1 = 1:m
  C(x1) = getPX(P,m,n,x1,1);
end

return