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

Full-text PDF Free Access

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