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

Full-text PDF Free Access

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 and . 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