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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 89, 2017 - Issue 1: Festschrift for Bernt Øksendal
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Original Articles

Bounds for expected maxima of Gaussian processes and their discrete approximations

Konstantin BorovkovSchool of Mathematics and Statistics, The University of Melbourne, Parkville, Australia.View further author information
,
Yuliya MishuraMechanics and Mathematics Faculty, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.Correspondence[email protected]
View further author information
,
Alexander NovikovSchool of Mathematical and Physical Sciences, University of Technology Sydney, Sydney, Australia.;Steklov Institute of Mathematics, Moscow, Russia.View further author information
&
Mikhail ZhitlukhinSteklov Institute of Mathematics, Moscow, Russia.View further author information
Pages 21-37 | Received 02 Aug 2015, Accepted 26 Nov 2015, Published online: 30 Dec 2015

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Hossein Jafari & Yiqiang Q. Zhao. (2021) Bounds for the expected supremum of some non-stationary Gaussian processes. Stochastics 0:0, pages 1-23.
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B. L. S. Prakasa Rao. (2020) More on maximal inequalities for sub-fractional Brownian motion. Stochastic Analysis and Applications 38:2, pages 238-247.
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Krzysztof Bisewski & Grigori Jasnovidov. (2023) On the speed of convergence of Piterbarg constants. Queueing Systems 105:1-2, pages 129-137.
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Anatoliy Malyarenko, Yuliya Mishura, Kostiantyn Ralchenko & Sergiy Shklyar. (2023) Entropy and alternative entropy functionals of fractional Gaussian noise as the functions of Hurst index. Fractional Calculus and Applied Analysis 26:3, pages 1052-1081.
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Krzysztof Bisewski. (2023) Lower bound for the expected supremum of fractional brownian motion using coupling. Journal of Applied Probability, pages 1-17.
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David Baños, Martin Bauer, Thilo Meyer-Brandis & Frank Proske. (2023) Restoration of Well-Posedness of Infinite-Dimensional Singular ODE’s via Noise. Potential Analysis.
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Tomonori Nakatsu. (2023) On density functions related to discrete time maximum of some one-dimensional diffusion processes. Applied Mathematics and Computation 441, pages 127672.
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Yuliya Mishura, Kostiantyn Ralchenko & Sergiy Shklyar. (2023) Gaussian Volterra processes: Asymptotic growth and statistical estimation. Theory of Probability and Mathematical Statistics 108:0, pages 149-167.
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Krzysztof Bisewski, Krzysztof Dȩbicki & Tomasz Rolski. (2022) Derivative of the expected supremum of fractional Brownian motion at $$H=1$$. Queueing Systems 102:1-2, pages 53-68.
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Nour Al Hayek, Illia Donhauzer, Rita Giuliano, Andriy Olenko & Andrei Volodin. (2021) Asymptotics of Running Maxima for φ-Subgaussian Random Double Arrays. Methodology and Computing in Applied Probability 24:3, pages 1341-1366.
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Krzysztof Bisewski, Krzysztof Dȩbicki & Tomasz Rolski. (2022) Derivatives of sup-functionals of fractional Brownian motion evaluated at H= 12. Electronic Journal of Probability 27:none.
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Krzysztof Bisewski, Krzysztof Dębicki & Michel Mandjes. (2021) Bounds for expected supremum of fractional Brownian motion with drift. Journal of Applied Probability 58:2, pages 411-427.
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Giacomo Ascione, Yuliya Mishura & Enrica Pirozzi. (2019) Fractional Ornstein-Uhlenbeck Process with Stochastic Forcing, and its Applications. Methodology and Computing in Applied Probability 23:1, pages 53-84.
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I. A. Kozik & V. I. Piterbarg. (2021) High Excursions of Gaussian Nonstationary Processes in Discrete Time. Journal of Mathematical Sciences 253:6, pages 867-874.
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Artagan Malsagov & Michel Mandjes. (2019) Approximations for reflected fractional Brownian motion. Physical Review E 100:3.
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. (2019) Тезисы докладов, представленных на Третьей Международной конференции по стохастическим методамThird International Conference on Stochastic Methods (Abstracts). Теория вероятностей и ее применения Teoriya Veroyatnostei i ee Primeneniya 64:1, pages 151-204.
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Nino E. Kordzakhia, Yury A. Kutoyants, Alexander A. Novikov & Lin-Yee Hin. (2018) On limit distributions of estimators in irregular statistical models and a new representation of fractional Brownian motion. Statistics & Probability Letters 139, pages 141-151.
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Alexander I Bufetov & Andrey V Dymov. (2018) A Functional Limit Theorem for the Sine-Process. International Mathematics Research Notices.
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Konstantin Borovkov, Yuliya Mishura, Alexander Novikov & Mikhail Zhitlukhin. (2018) New and refined bounds for expected maxima of fractional Brownian motion. Statistics & Probability Letters 137, pages 142-147.
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Konstantin Borovkov & Mikhail Zhitlukhin. (2018) On the maximum of the discretely sampled fractional Brownian motion with small Hurst parameter. Electronic Communications in Probability 23:none.
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. 2018. Stochastic Analysis of Mixed Fractional Gaussian Processes. Stochastic Analysis of Mixed Fractional Gaussian Processes 185 192 .
A. N. Shiryaev, I. V. Pavlov, T. B. Tolozova & V. V. Shamraeva. (2017) Abstracts of the International Conference on Stochastic Methods. Theory of Probability & Its Applications 61:3, pages 521-538.
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