algorithm simulate markov chain inputnumber of steps ninitial pdf transition density draw from the initial pdf for to do draw xt from the distribution corresponding to the density (xt- return xn example (markov chain simulationfor time-homogeneous markov chains with discrete state spacewe can visualize the one-step transitions by means of transition graphwhere arrows indicate possible transitions between states and the labels describe the corresponding probabilities figure shows (on the leftthe transition graph of the markov chain {xt with state space { and one-step transition matrix transition graph figure the transition graph (leftand typical path (rightof the markov chain in the same figure (on the righta typical outcome (pathof the markov chain is shown the path was simulated using the python program below in this implementation the markov chain always starts in state we will revisit markov chainsand in particular markov chains with continuous state spacesin section mcsim py import numpy as np import matplotlib pyplot as plt np array ([[ [ ][ ][ ]] np array (np ones(ndtype =int) [ for in range ( , - )