Theory of Probability and Mathematical Statistics

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

Author(s): T. V. Kadankova
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 70 (2004).
Journal: Theor. Probability and Math. Statist. No. 70 (2005), 61-70.
MSC (2000): Primary 60J25, 60J75
Posted: August 5, 2005
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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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Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60J25, 60J75

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

DOI: 10.1090/S0094-9000-05-00631-9
PII: S 0094-9000(05)00631-9
Received by editor(s): 21/MAR/2003
Posted: August 5, 2005
Copyright of article: Copyright 2005, American Mathematical Society

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ISSN: 1547-7363(e) 0094-9000(p)

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