For a two--dimensional random walk with correlated components the first crossing time probability problem through unit-slope straight lines is analyzed. The p.g.f.'s for the first-crossing-time probabilities are expressed as solution of a fourth-degree algebraic equation and are then exploited to obtain the first-crossing-time probabilities. Several additional results, including the mean first-crossing time and the probability of ultimate crossing, are also given.
On some first-crossing-time probabilities for a two-dimensional random walk with correlated components
DI CRESCENZO, Antonio;GIORNO, Virginia;NOBILE, Amelia Giuseppina
1992-01-01
Abstract
For a two--dimensional random walk with correlated components the first crossing time probability problem through unit-slope straight lines is analyzed. The p.g.f.'s for the first-crossing-time probabilities are expressed as solution of a fourth-degree algebraic equation and are then exploited to obtain the first-crossing-time probabilities. Several additional results, including the mean first-crossing time and the probability of ultimate crossing, are also given.File in questo prodotto:
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