Results are out! Find what you need...fast. Get quick advice or join the chat
Hey! Sign in to get help with your study questionsNew here? Join for free to post

Markov chain help

Announcements Posted on
Will you get the grades you need for uni? Get prepared today and de-stress, sign up to email alerts for course places! 02-06-2015
Waiting on IB results? Our IB results hub explains everything you need to know 01-06-2015
  1. Offline

    ReputationRep:
    Just a quick couple of questions:
    1
    What is meant by the 'equilibrium distribution vector' concerning a Markov chain of probabilities?

    Take this example:

    1---------2----------3

    "An object moves along the graph shown above, so that at each step it moves with equal probability to a neighbouring point."

    a) Write down the transition matrix P for this Markov process (i think i've got this right, so i'm not bothered about this one)
    b) Calculate the equilibrium distribution vector for this Markov process.

    2
    How do you calculate the limit as n -> infinity of A^n for a square matrix A?
  2. Offline

    ReputationRep:
    From my rather hazy memory, an equilibrium (or invariant) distribution vector is a stochastic row vector \pi with \pi P = \pi.
  3. Offline

    ReputationRep:
    (Original post by generalebriety)
    From my rather hazy memory, an equilibrium (or invariant) distribution vector is a stochastic row vector \pi with \pi P = \pi.
    Thanks, that makes sense now.
  4. Offline

    ReputationRep:
    In general, finding \lim_{n\to\infty} A^n is tricky (even assuming the limit exists).

    But barring a few pathological cases(*), if M is a stochastic matrix, and \pi is an invariant vector for M, then M^n x \to \pi \for all x. Which means M^n converges to the matrix with all columns equal to \pi.

    (*) I think it always works as longs as M has no elements of size 1, but that's intuition and hope speaking rather than detailed knowledge.

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: February 12, 2009
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

New on TSR

It's IB results day tomorrow

Check out our IB results hub here & get prepared here

Study resources
x

Think you'll be in clearing or adjustment?

Hear direct from unis that want to talk to you

Get email alerts for university course places that match your subjects and grades. Just let us know what you're studying.

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.