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 B1 particles. Call this latter move a 0jump. Ultimately the process will reach the absorbing state with all particles in position K . Let N be the random total number of 0jumps made. Prove E Â± B1 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
 Reed
 Markov chain, irreducible Markov chain, markov transition matrix, nonhomogeneous Markov chain

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