Advanced search
Publication Cover
Stochastics
An International Journal of Probability and Stochastic Processes
Volume 89, 2017 - Issue 1: Festschrift for Bernt Øksendal
Submit an article Journal homepage
273
Views
22
CrossRef citations to date
0
Altmetric
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

Citations (22)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (2)

Hossein Jafari & Yiqiang Q. Zhao. (2021) Bounds for the expected supremum of some non-stationary Gaussian processes. Stochastics 0:0, pages 1-23.
Read now
B. L. S. Prakasa Rao. (2020) More on maximal inequalities for sub-fractional Brownian motion. Stochastic Analysis and Applications 38:2, pages 238-247.
Read now

Articles from other publishers (20)

Krzysztof Bisewski & Grigori Jasnovidov. (2023) On the speed of convergence of Piterbarg constants. Queueing Systems 105:1-2, pages 129-137.
Crossref
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.
Crossref
Krzysztof Bisewski. (2023) Lower bound for the expected supremum of fractional brownian motion using coupling. Journal of Applied Probability, pages 1-17.
Crossref
David Baños, Martin Bauer, Thilo Meyer-Brandis & Frank Proske. (2023) Restoration of Well-Posedness of Infinite-Dimensional Singular ODE’s via Noise. Potential Analysis.
Crossref
Tomonori Nakatsu. (2023) On density functions related to discrete time maximum of some one-dimensional diffusion processes. Applied Mathematics and Computation 441, pages 127672.
Crossref
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.
Crossref
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.
Crossref
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.
Crossref
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.
Crossref
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.
Crossref
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.
Crossref
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.
Crossref
Artagan Malsagov & Michel Mandjes. (2019) Approximations for reflected fractional Brownian motion. Physical Review E 100:3.
Crossref
. (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.
Crossref
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.
Crossref
Alexander I Bufetov & Andrey V Dymov. (2018) A Functional Limit Theorem for the Sine-Process. International Mathematics Research Notices.
Crossref
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.
Crossref
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.
Crossref
. 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.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Supercharge Your Next Research Paper: Research and write your next paper with Jenni AI.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.