A state is a <recurrent state> if the <probability> of a return at some positive time, starting there, is one. It is a <transient state> if that return <probability> is less than one. It is an <absorbing state> if its one-step <probability> of remaining there is one. An <absorbing state> is recurrent, since every subsequent time is a return.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2011 / M / M5 / a / iii / Solution

 Solution (source code)