Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

2000 • Question 8

Question

Math 6010 • Linear Models 2000 • Question 8

Consider the Markov chain in the set of nonnegative integers with transitions \(P(n,0)=1-P(n,n+1)=p_n>0\) for each \(n\ge 0\). Give necessary and sufficient conditions on the sequence \(\{p_n\}\) for the chain to be (a) positive recurrent, (b) null recurrent, and (c) transient.

Raw LaTeX

Consider the Markov chain in the set of nonnegative integers with
transitions \(P(n,0)=1-P(n,n+1)=p_n>0\) for each \(n\ge 0\). Give necessary and
sufficient conditions on the sequence \(\{p_n\}\) for the chain to be
\textbf{(a)} positive recurrent, \textbf{(b)} null recurrent, and \textbf{(c)}
transient.

Topic Tags

Markov Chains and Recurrence Uniform Integrability and Truncation Methods