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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

2000 • Question 7

Question

Math 6010 • Linear Models 2000 • Question 7

Let \(P\) be the transition matrix for a finite irreducible aperiodic Markov chain, and assume that \(P\) is doubly stochastic (row and column sums are 1). Find the limit \(\lim _{n\to \infty }P_{ij}^n\) for all \(i\) and \(j\), and provide justification.

Raw LaTeX

Let \(P\) be the transition matrix for a finite irreducible aperiodic
Markov chain, and assume that \(P\) is doubly stochastic (row and column sums are 1).
Find the limit \(\lim_{n\to\infty}P_{ij}^n\) for all \(i\) and \(j\), and provide
justification.

Topic Tags

Brownian Motion and Stochastic Processes Markov Chains and Recurrence Uniform Integrability and Truncation Methods