Results 1 to 4 of 4

Math Help - Transition Matrix - Stationary Distribution

  1. #1
    Newbie
    Joined
    Aug 2009
    Posts
    21

    Transition Matrix - Stationary Distribution

    Consider the one-step transition matrix

    P = \begin{pmatrix} q & p & 0 \\0 & q & p \\ p & 0 & q \\ \end{pmatrix}

    where q = 1 - p and 0 < p < 1.

    Find all stationary distributions of a chain with state space E = \{0,1,2\} and one-step transition matrix P.

    Are any stationary distributions also limiting distributions?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Aug 2009
    Posts
    21
    My mid-term is in two days and I really need to understand how to calculate this sort of question.

    I have.....
    The equation \pi = \pi P becomes

    \pi_0 = q \pi_0 + p \pi_1

    \pi_1 = q \pi_1 + p \pi_2

    \pi_2 = p \pi_0 + q \pi_2

    I really dont know how to get the solutions from here.
    Last edited by RoyalFlush; September 14th 2009 at 07:41 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2009
    Posts
    13
    i think,

     \pi_0 + \pi_1 + \pi_2 = 1

    so you can just make one of the  \pi the subject and then sub it into the 3 equations that you found yeah and continue until you found all the values of  \pi
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Aug 2009
    Posts
    21
    I think my talent for mathematics has just about run its course

    I get

    \pi_2 = \frac{p-p\pi_1}{1-p+q}, \pi_1 = \frac{\pi_2 - p - q\pi_2}{1-q-p} and \pi_0 = \frac{\pi_1 - q\pi_1 - \pi_2 +p+q\pi_2}{1-q}

    Im confused with the difference between the limiting distribution and the stationary distribution???? Can anyone please explain this?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Transition Matrix
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 22nd 2011, 12:31 AM
  2. Find limiting distribution of transition matrix
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 16th 2011, 03:19 PM
  3. Transition matrix
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 21st 2009, 05:23 PM
  4. Transition Matrix
    Posted in the Statistics Forum
    Replies: 1
    Last Post: September 5th 2009, 06:37 PM
  5. Calculating Stationary Distribution with Matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 7th 2006, 04:43 AM

Search Tags


/mathhelpforum @mathhelpforum