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Trudy Mat. Inst. Steklova, 2014, Volume 287, Pages 162–181 (Mi tm3575)  

This article is cited in 4 scientific papers (total in 4 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

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).


DOI: https://doi.org/10.1134/S0371968514040104

Full text: PDF file (335 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 287:1, 155–173

Bibliographic databases:

UDC: 519.216
Received in February 2014

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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\paper Sharp maximal inequalities for stochastic processes
\inbook Stochastic calculus, martingales, and their applications
\bookinfo Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2014
\vol 287
\pages 162--181
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    This publication is cited in the following articles:
    1. Theory Probab. Appl., 61:1 (2017), 159–167  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Ch. Jia, “Sharp moderate maximal inequalities for upward skip-free Markov chains”, J. Theor. Probab., 32:3 (2019), 1382–1398  crossref  mathscinet  isi
    3. Jia Ch., Zhao G., “Moderate Maximal Inequalities For the Ornstein-Uhlenbeck Process”, Proc. Amer. Math. Soc., 148:8 (2020), 3607–3615  crossref  mathscinet  isi
    4. N. E. Kordzakhia, A. A. Novikov, “On maximal inequalities for Ornstein–Uhlenbeck processes with jumps”, Teoriya veroyatn. i ee primen., 66:4 (2021), 895–913  mathnet  crossref
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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