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On the joint distribution of the supremum, infimum, and the value of a semicontinuous process with independent increments


Author: T. V. Kadankova
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 70 (2004).
Journal: Theor. Probability and Math. Statist. 70 (2005), 61-70
MSC (2000): Primary 60J25, 60J75
DOI: https://doi.org/10.1090/S0094-9000-05-00631-9
Published electronically: August 5, 2005
MathSciNet review: 2109824
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Abstract | References | Similar Articles | Additional Information

Abstract: The joint distribution of the supremum, infimum, and the value of a homogeneous lower semicontinuous process with independent increments is found in this paper.

The weak convergence of the boundary distribution to the corresponding distribution of the Wiener process is proved in the case of $\mathsf{E}\xi(1)=0$ and $\mathsf{E}\xi^{2}(1)<\infty$. Exact and asymptotic relations are obtained for this distribution.


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Additional Information

T. V. Kadankova
Affiliation: Mechanics and Mathematics Faculty, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine

DOI: https://doi.org/10.1090/S0094-9000-05-00631-9
Received by editor(s): March 21, 2003
Published electronically: August 5, 2005
Article copyright: © Copyright 2005 American Mathematical Society

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