Reference no: EM13966532
(Constructing Examples). Construct an example of each of the following phenomena:
(a) a Markov chain with only absorbing states;
(b) a Markov chain that is irreducible but not regular;
(c) a Markov chain that is irreducible but not aperiodic;
(d) a Markov chain on an infinite state space that is irreducible and aperiodic, but not regular;
(e) a Markov chain in which there is at least one null recurrent state;
(f) a Markov chain on an infinite state space such that every state is transient;
(g) a Markov chain such that each first-passage time Tij has all moments finite;
(h) a Markov chain without a proper stationary distribution;
(i) independent irreducible chains fXng; fYng, such that Zn D .Xn; Yn/ is not irreducible;
(j) Markov chains fXng; fYng such that Zn D .Xn; Yn/ is not a Markov chain.
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