Exam 12: Markov Process Models

Markov processes are a powerful decision making tool useful in explaining the behavior of systems and determining limiting behavior.

Once a process reaches steady-state, the state probabilities will never change.

"How you arrived at where you are now has no bearing on where you go next." This, simply put, is the Markovian memoryless property.

All Markov processes exhibit some form of periodicity.

A state vector is used for determining the:

Is this an acceptable transition matrix? Explain your answer. | .3 .3 .4 0 | | .2 .5 0 .3 | | .1 .6 .2 .1 |

Which of the following is a necessary characteristic of a Markovian transition matrix?

What is the minimum percentage of transition probabilities that must be nonzero?

The values towards which state probabilities converge are the steady-state probabilities.

Although the number of possible states in a Markov process may be infinite, they must be countably infinite.

The "mean recurrence time" for a state in a Markov process:

This transition matrix represents what type of Markov process?

All of the following are necessary characteristics of a Markov process except:

The state vector for stage j of a Markov chain with n states:

State probabilities for any given stage must sum to 1.

Charles dines out twice a week.On Tuesdays, he always frequents the same Mexican restaurant; on Thursdays, he randomizes between Greek, Italian, or Thai (but never Mexican).Is this transient, periodic, or recurrent behavior?

Define these Excel functions:

In a Markovian system, is it possible to have only one absorbing state?

A firm displeased with its projected steady-state market share may try to improve the situation by taking steps which hopefully will:

In a Markovian transition matrix, each column's probabilities sum to 1.