Stochastic

Any matrix with properties i and ii gives rise to a

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Xn . To construct the chain we can think of playing a board game. When we are in state i, we roll a die (or generate a random number on a computer) to pick the next state, going to j with probability p(i, j ). Example 1.3. Weather chain. Let Xn be the weather on day n in Ithaca, NY, which we assume is either: 1 = rainy, or 2 = sunny. Even though the weather is not exactly a Markov chain, we can propose a Markov chain model for the weather by writing down a transition probability 1 .6 .2 1 2 2 .4 .8 The table says, for example, the probability a rainy day (state 1) is followed by a sunny day (state 2) is p(1, 2) = 0.4. A typical question of interest is: Q. What is the long-run fraction of days that are sunny? Example 1.4. Social mobility. Let Xn be a family’s social class in the nth generation, which we assume is either 1 = lower, 2 = middle, or 3 = upper. In our simple version of sociology, changes of status are a Markov chain with the following transition probability 1 2 3 1 .7 .3 .2 2 .2 .5 .4 3 .1 .2 .4 Q. Do the fractions of people in the thre...
View Full Document

This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.

Ask a homework question - tutors are online