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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Optimal stopping time problem for random walks with polynomial reward functions


Authors: Yu. S. Mishura and V. V. Tomashyk
Translated by: O. I. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 86 (2012).
Journal: Theor. Probability and Math. Statist. 86 (2013), 155-167
MSC (2010): Primary 60G40, 60G50
Published electronically: August 20, 2013
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Abstract: The optimal stopping time problem for random walks with a drift to the left and with a polynomial reward function is studied by using the Appel polynomials. An explicit form of optimal stopping times is obtained.


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Additional Information

Yu. S. Mishura
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 4E, Kiev 03127, Ukraine
Email: myus@univ.kiev.ua

V. V. Tomashyk
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 4E, Kiev 03127, Ukraine
Email: vladdislav@gmail.com

DOI: http://dx.doi.org/10.1090/S0094-9000-2013-00895-3
PII: S 0094-9000(2013)00895-3
Keywords: Appel polynomials, random walks, reward functions, stopping times
Received by editor(s): May 11, 2011
Published electronically: August 20, 2013
Article copyright: © Copyright 2013 American Mathematical Society