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Theory of Probability and Mathematical Statistics

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Two-boundary problems for a random walk with negative geometric jumps


Author: T. V. Kadankova
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 68 (2003).
Journal: Theor. Probability and Math. Statist. 68 (2004), 55-66
MSC (2000): Primary 60G50, 60J50
DOI: https://doi.org/10.1090/S0094-9000-04-00604-0
Published electronically: June 10, 2004
MathSciNet review: 2000395
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Abstract | References | Similar Articles | Additional Information

Abstract: Two-boundary problems for a random walk with negative geometric jumps are considered, and the corresponding results for a usual semicontinuous random walk are generalized for them. The following results are obtained: the probability distribution of ruin is found and expressed in terms of the lower and upper boundaries; formulas are given for the joint distribution of the infimum, supremum, and the walk itself at an arbitrary time instance; the transient probabilities and ergodic distribution are evaluated for the process describing the evolution of the random walk with two boundaries.


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Additional Information

T. V. Kadankova
Affiliation: Faculty for Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv, Ukraine
Email: t_thys@ukr.net

DOI: https://doi.org/10.1090/S0094-9000-04-00604-0
Received by editor(s): September 27, 2002
Published electronically: June 10, 2004
Article copyright: © Copyright 2004 American Mathematical Society