Abstract
For a homogeneous process with independent increments, we determine the integral transforms of the joint distribution of the first-exit time from an interval and the value of a jump of a process over the boundary at exit time and the joint distribution of the supremum, infimum, and value of the process.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1359–1384, October, 2005.
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Kadankov, V.F., Kadankova, T.V. On the distribution of the time of the first exit from an interval and the value of a jump over the boundary for processes with independent increments and random walks. Ukr Math J 57, 1590–1620 (2005). https://doi.org/10.1007/s11253-006-0016-6
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DOI: https://doi.org/10.1007/s11253-006-0016-6