Two-boundary problems for a Poisson process with exponentially distributed component |
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Authors: | V F Kadankov T V Kadankova |
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Institution: | (1) Institute of Mathematics, Ukrainian Academy of Sciences, Kiev;(2) Shevchenko Kiev National University, Kiev |
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Abstract: | For a Poisson process with exponentially distributed negative component, we obtain integral transforms of the joint distribution
of the time of the first exit from an interval and the value of the jump over the boundary at exit time and the joint distribution
of the time of the first hit of the interval and the value of the process at this time. On the exponentially distributed time
interval, we obtain distributions of the total sojourn time of the process in the interval, the joint distribution of the
supremum, infimum, and value of the process, the joint distribution of the number of upward and downward crossings of the
interval, and generators of the joint distribution of the number of hits of the interval and the number of jumps over the
interval.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 7, pp. 922–953, July, 2006. |
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Keywords: | |
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