First passage time densities for random walk spans |
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Authors: | George H Weiss Edmund A DiMarzio Richard J Gaylord |
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Institution: | (1) National Institutes of Health, 20205 Bethesda, Maryland;(2) National Bureau of Standards, 20899 Gaithersburg, Maryland;(3) Polymer Group, Department of Metallurgy, University of Illinois at Urbana-Champaign, 1304 West Green Street, 61801 Urbana, Illinois |
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Abstract: | A general expression is derived for the Laplace transform of the probability density of the first passage time for the span of a symmetric continuous-time random walk to reach levelS. We show that when the mean time between steps is finite, the mean first passage time toS is proportional toS
2. When the pausing time density is asymptotic to a stable density we show that the first passage density is also asymptotically stable. Finally when the jump distribution of the random walk has the asymptotic formp(j) A/|j|
+1, 0 < < 2 it is shown that the mean first passage time toS goes likeS
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Keywords: | Random walks spans stable laws |
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