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Proceedings of the Steklov Institute of Mathematics

, Volume 287, Issue 1, pp 155–173 | Cite as

Sharp maximal inequalities for stochastic processes

  • Ya. A. LyulkoEmail author
  • A. N. Shiryaev
Article

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.

Keywords

Brownian Motion Random Walk Function Versus STEKLOV Institute Mathematical Expectation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.International Laboratory of Quantitative FinanceNational Research University Higher School of EconomicsMoscowRussia
  2. 2.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  3. 3.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia

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