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Theory of Probability and Mathematical Statistics

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Evaluation of extreme values of entropy functionals


Authors: Yu. S. Mishura and H. S. Zhelezniak
Translated by: N. N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 99 (2018).
Journal: Theor. Probability and Math. Statist. 99 (2019), 199-210
MSC (2010): Primary 60G22, 60J65; Secondary 94A17
DOI: https://doi.org/10.1090/tpms/1090
Published electronically: February 27, 2020
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the sum of two independent Wiener processes with a drift and construct a family of probability measures such that the drift with respect to each of them is zero. Among these measures, we search for those that minimize or maximize certain functionals, for example, entropy-type functionals.


References [Enhancements On Off] (What's this?)

  • [1] H. Föllmer and A. Schied, Stochastic Finance: An Introduction in Discrete Time, Walter de Gruyter, Berlin, 2002, pp. 121-130. MR 1925197
  • [2] C. Leonard, Minimization of entropy functionals, J. Math. Anal. Appl. 346 (2008), no. 1, 183-204. MR 2428283
  • [3] Y. Mishura and H. Zhelezniak, Extreme measures for entropy functionals, Bull. Taras Shevchenko National University of Kyiv. Series: Physics & Mathematics (2017), no. 4, 15-20.

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Additional Information

Yu. S. Mishura
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: myus@univ.kiev.ua

H. S. Zhelezniak
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: hanna.zhelezniak@gmail.com

DOI: https://doi.org/10.1090/tpms/1090
Keywords: Wiener process, Radon--Nikodym derivative, entropy functional, minimization, maximization
Received by editor(s): October 15, 2018
Published electronically: February 27, 2020
Article copyright: © Copyright 2020 American Mathematical Society