Results 1 to 2 of 2

Math Help - Markov Property

  1. #1
    Newbie
    Joined
    Aug 2010
    Posts
    3

    Markov Property

    one more question,

    I am rereading a lecture and i come across the following:
    define escape time as \xi_r=inf[t>0 | (||X_t-X_0||>r)]
    now my notes say that is easy to show by using markov property that P[\xi_r \geq nt]\leq p^n for n=0,1,..
    By the time i must have thought it was easy, now i cant remember how to do it anymore
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Aug 2010
    Posts
    3
    i found it again:
    P[\xi_r \geq nt]\leq P_x \cap_{k\leq n}[X_{kt} \in B_x(r)]=(P_t^d[x \in B_x(r)])^n \leq p^n where B_x(r) is closed ball of radius r around x
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof that summation of N Markov processes is a Markov process
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 28th 2011, 08:44 AM
  2. Markov Chain of random variables from a primitive markov chain
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 19th 2011, 09:12 AM
  3. Mean Value Property Implies "Volume" Mean Value Property
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: March 16th 2011, 09:13 PM
  4. Property of a Markov Chain
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 8th 2010, 10:55 AM
  5. Replies: 2
    Last Post: October 28th 2008, 07:32 PM

Search Tags


/mathhelpforum @mathhelpforum