Unformatted text preview: game, as follows. A state i is chosen at random according to π ; the cat and mouse are both placed at i , but before the cat can do anything the mouse jumps to another state chosen according to p ( i, · ). Thereafter, the mouse doesn’t move. The cat now searches for the mouse by moving at random according to the “timereversed” Markov chain, i.e. the chain with transition matrix q ( i,j ) = π ( j ) p ( j,i ) /π ( i ) . Find a simple formula for the expected number of steps taken by the cat until it ﬁnds the mouse. 4...
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 Spring '09
 Reed
 Markov Chains, Markov chain, π, irreducible Markov transition

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