Homework 9

Consider the following Markov process: It takes values on {0,1,2} and has transition matrix \[ P = \begin{bmatrix} 0 & 1 & 0 \\ \frac12 & 0 & \frac12 \\ 0 & 1 & 0 \\ \end{bmatrix} \] Find the spectral decomposition P=UDU^-1. Find the the n-step transition matrix and the stationary distribution of this process both analytically and via a simulation.