Unformatted text preview: X is as follows. Pick one of the particles uniformly at random, and let it perform a move according to P ( Â· , Â· ). If the move takes the particle to a position which is not 0, that concludes the step of X . Otherwise the particle tries to move to 0, in which case it is immediately replaced at the position of another particle, picked uniformly at random from the other B-1 particles. Call this latter move a 0-jump. Ultimately the process will reach the absorbing state with all particles in position K . Let N be the random total number of 0-jumps made. Prove E Â± B-1 B Â² N = i K . What can you deduce about EN ? [Hint: Let A n be the average position of the B particles after n steps. Find a martingale related to A n .] 6...
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- Spring '09
- Markov chain, irreducible Markov chain, markov transition matrix, non-homogeneous Markov chain