The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Math Topics » alt.math.undergrad

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Markov equilibrium
Replies: 2   Last Post: Apr 23, 2013 6:21 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 1,412
Registered: 12/3/04
Re: Markov equilibrium
Posted: Apr 23, 2013 6:21 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article
RichD <> wrote:

> As I understand it, a Markov process is a probabilisitic
> sequence of state transiitons. It's completely specified
> by the state transition matrix.
> However, I sometimes see references to the
> equlibrium condition, whether it's been reached,
> etc. I don't get this, can anyone elaborate? ....

Example (using row vector notation). Transition matrix A =

(1/3 2/3)
(1/2 1/2).

Suppose the system has state vector (x y), i.e. there is
probability x that it is in the first state, and y for the second.
Then the next step of the process takes it to (x y)A. If you choose
some initial probabilities x and y, and iterate through quite a few
steps, you will find the state vector getting closer and closer to (3/7
4/7). If the systen were actually in that state, then the next step
would take it to (3/7 4/7)A which is again equal to (3/7 4/7).
(Work it out!)

(3/7 4/7) describes the equilibrium state, and this particular
process converges steadily towards that state. (Some others don't.)
You may be able to see that the equilibrium state vector is an
eigenvector of A corresponding to the eigenvalue 1.


Ken Pledger.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.