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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Volume 287, Pages 162–181
DOI: https://doi.org/10.1134/S0371968514040104 (Mi tm3575) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Sharp maximal inequalities for stochastic processes

Ya. A. Lyulkoa, A. N. Shiryaevbc

a National Research University "Higher School of Economics", Moscow, Russia
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia
c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Full-text PDF (335 kB) Citations (5)
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DOI: https://doi.org/10.1134/S0371968514040104
Abstract: This work is a survey of existing methods and results in the problem of estimating the mathematical expectation of the maximum of a random process up to an arbitrary Markov time. Both continuous-time (standard Brownian motion, skew Brownian motion, Bessel processes) and discrete-time (symmetric Bernoulli random walk and its modulus) processes are considered.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.A12.31.0007
Russian Foundation for Basic Research 14-01-00739
This work was supported by the International Laboratory of Quantitative Finance, National Research University Higher School of Economics (contract no. 14.A12.31.0007 with the Ministry of Education and Science of the Russian Federation), and by the Russian Foundation for Basic Research (project no. 14-01-00739).
Received in February 2014
English version:
Proceedings of the Steklov Institute of Mathematics, 2014, Volume 287, Issue 1, Pages 155–173
DOI: https://doi.org/10.1134/S0081543814080100
Bibliographic databases:
Document Type: Article
UDC: 519.216
Language: Russian
Citation: Ya. A. Lyulko, A. N. Shiryaev, “Sharp maximal inequalities for stochastic processes”, Stochastic calculus, martingales, and their applications, Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 287, MAIK Nauka/Interperiodica, Moscow, 2014, 162–181; Proc. Steklov Inst. Math., 287:1 (2014), 155–173
Citation in format AMSBIB
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\bookinfo Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
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\vol 287
\pages 162--181
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\publaddr Moscow
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    • This publication is cited in the following 5 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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