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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

1996 • Question 4

Question

Math 6010 • Linear Models 1996 • Question 4

Consider the Markov chain in the state space \(S=\{\ldots ,-2,-1,0,1,2,\ldots \}\) with transitions \(P(i,i+2)=p\) and \(P(i,i-1)=1-p\), where \(0<p<1\). Determine for which \(p\) this chain is recurrent and for which \(p\) it is transient.

Raw LaTeX

Consider the Markov chain in the state space
\(S=\{\ldots,-2,-1,0,1,2,\ldots\}\) with transitions \(P(i,i+2)=p\) and
\(P(i,i-1)=1-p\), where \(0<p<1\). Determine for which \(p\) this chain is recurrent
and for which \(p\) it is transient.

Topic Tags

Markov Chains and Recurrence Uniform Integrability and Truncation Methods