On page 20 the formula before 5.8, may I know where did the first term on the RHS come from? It says that the RHS is obtained by applying equation 5.7, but whichever of the two does not give me that first term. Thanks.
hi actuaryre If i understand you correctly, it's basically splitting out p_ij(t + h) = sum_k {p_ik (t) p_kj (h)} into two parts via reasoning, and not directly substituting in 5.7. So: sum_(k neq j){ (p_ik (t)h mu_ij } means the sum of all transitions where k and i does not equal j (ie: it ends up elsewhere) plus p_ij(t)( 1 + h mu_jj) which means it ends up in the same state (i=j) plus o(h) which is some constant we're not worried about. Correct?
