Its previous states can only be S(w - 1, i) (0 [less than or equal to] i < w-1), and if AU increases to w-1 earlier than VW increases to w, S(w-1, i) will transfer to
absorbing state S(w-1, w-1), otherwise S(w-1, i) will transfers to S(w, j) (i [less than or equal to] j [less than or equal to] w-2) and will not transfer to S(w, w-1) due to conclusion-2.
Absorbing states could be reached either by collection or bad debt, both of which lead to a decline in the portfolio size.
Once an
absorbing state is entered the process remains in that state and cannot exit.
For a diminishing urn we obtain that the sum of the weights of all possible paths starting at state (m, n) and ending at the
absorbing state (i, j) [member of] A (which did not pass another
absorbing state earlier) gives then the required probability, that when starting at (m, n) we are ending at (i, j).
That hasn't gone over well with some members of the academic community, who believe spending on athletics has gotten out of control - particularly when the school is
absorbing state budget cuts.
Despite recent efforts in the Netherlands to lower the proportion of people falling into inactivity and benefit dependency, inactivity seems to have become a more and more
absorbing state when one analyses the flows from one labour market status into another (Appendix A).
Some interaction can be modelled by treating entities which leave the system as entering an
absorbing state.
