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Markov chains in small time intervals
Published online by Cambridge University Press: 14 July 2016
Abstract
For a time-homogeneous continuous-parameter Markov chain we show that as t → 0 the transition probability pn,j (t) is at least of order where r(n, j) is the minimum number of jumps needed for the chain to pass from n to j. If the intensities of passage are bounded over the set of states which can be reached from n via fewer than r(n, j) jumps, this is the exact order.
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- Short Communications
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- Copyright © Applied Probability Trust
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