Unformatted text preview: X n ) is recurrent. (c) Assuming recurrence, ﬁnd the relation between the P-invariant measure and the Q-invariant measure. (d) Deduce that, on an inﬁnite state space, it is possible for ( Y n ) to be positive-recurrent while ( X n ) is not. 5. Let X n be an ﬁnite irreducible chain with transition matrix P . Fix a subset A of S . Deﬁne a transition matrix Q on A by q ( i,j ) = p ( i,j ) / X k ∈ A p ( i,k ) . Suppose Q is irreducible. In the case where P is reversible , ﬁnd a simple explicit formula for the stationary distribution π * of Q in terms of P and its stationary distribution π . Give an example to show that the formula may not hold in the non-reversible case. 2...
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- Spring '09
- Sets, Markov chain, ﬁnite irreducible chain