Excursions of vector-valued Gaussian stochastic processes: exact asymptotics

2018/31/B/ST1/00370

Keywords

Descriptors

  • ST1_13: Rachunek prawdopodobieństwa i statystyka matematyczna

Panel

ST1 – Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution

Uniwersytet Wrocławski, Wydział Matematyki i Informatyki

Voivodeship: dolnośląskie

Other projects carried out by the institution »

Principal investigator (from the host institution)

prof. Krzysztof Grzegorz Dębicki

Number of co-investigators in the project: 3

Call

OPUS 16 – announced on 2018-09-14

Amount awarded
377 040 PLN
Project start date
2019-07-24
Project end date
2024-07-23
Project duration
60 months (the same as in the proposal)
Project status
Project settled

Project description

Download the project description in a pdf file

Note — project descriptions were prepared by the authors of the applications themselves and placed in the system in an unchanged form.

Information in the final report

Publication in academic press/journals (17)

  1. On Berman Functions

    Authors:
    Krzysztof Dębicki, Enkelejd Hashorva, Zbigniew Michna
    Academic press:
    Methodology and Computing in Applied Probability (year: 2024, volume: 1,08472222222222, pages: 46049), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s11009-023-10059-6 – link to the publication
  2. Derivative of the expected supremum of fractional Brownian motion at H=1

    Authors:
    Krzysztof Bisewski, Krzysztof Dȩbicki, Tomasz Rolski
    Academic press:
    Queueing Systems (year: 2022, volume: 102, pages: 53-68), Publisher: Springer US
    Status:
    Published
    DOI:
    10.1007/s11134-022-09859-3 – link to the publication
  3. Simultaneous ruin probability for multivariate Gaussian risk model

    Authors:
    Bisewski Krzysztof, Dębicki Krzysztof, Kriukov Nikolai
    Academic press:
    Stochastic Processes and their Applications (year: 2023, volume: 160, pages: 386-408), Publisher: Springer
    Status:
    Published
    DOI:
    10.1016/j.spa.2023.03.002 – link to the publication
  4. Sojourns of fractional Brownian motion queues: transient asymptotics

    Authors:
    Dębicki Krzysztof, Hashorva Enkelejd, Liu Peng
    Academic press:
    Queueing Systems (year: 2023, volume: 105, pages: 139-170), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s11134-023-09890-y – link to the publication
  5. Running supremum of Brownian motion in dimension 2: exact and asymptotic results

    Authors:
    Krzysztof Kępczyński
    Academic press:
    Stochastic Modles (year: 2022, volume: 38, pages: 116-129), Publisher: Taylor & Francis
    Status:
    Published
    DOI:
    10.1080/15326349.2021.1982395 – link to the publication
  6. Bounds for expected supremum of fractional Brownian motion with drift

    Authors:
    Krzysztof Bisewski, Krzysztof Dębicki, Michel Mandjes
    Academic press:
    Journal of Applied Probability (year: 2021, volume: 58, pages: 411-427), Publisher: Cambridge University Press
    Status:
    Published
    DOI:
    10.1017/jpr.2020.98 – link to the publication
  7. Sojourns of stationary Gaussian processes over a random interval

    Authors:
    Dębicki Krzysztof, Peng Xiaofan
    Academic press:
    ALEA-Latin Am. J. Probab. Math. (year: 2023, volume: 20, pages: 1017–1039), Publisher: IMS
    Status:
    Published
    DOI:
    10.30757/ALEA.v20-37 – link to the publication
  8. Sojourn times of Gaussian and related random fields

    Authors:
    Dębicki Krzysztof, Hashorva Enkelejd, Liu Peng, Michna Zbigniew
    Academic press:
    ALEA-Latin Am. J. Probab. Math. (year: 2023, volume: 20, pages: 249–289), Publisher: IMS
    Status:
    Published
    DOI:
    10.30757/ALEA.v20-10 – link to the publication
  9. Probability of entering an orthant by correlated fractional Brownian motion with drift: exact asymptotics

    Authors:
    Krzysztof Dębicki, Lanpeng Ji, Svyatoslav Novikov
    Academic press:
    Extremes (year: 2024, volume: 27, pages: 613–641), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s10687-024-00489-x – link to the publication
  10. Extremes of reflecting Gaussian processes on discrete grid

    Authors:
    Krzysztof Dębicki, Grigori Jasnovidov
    Academic press:
    Journal of Mathematical Analysis and Applications (year: 2024, volume: 532 (1), pages: 127952), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2023.127952 – link to the publication
  11. Finite-time ruin probability for correlated Brownian motions

    Authors:
    Krzysztof Dębicki, Enkelejd Hashorva, Konrad Krystecki
    Academic press:
    Scandinavian Actuarial Journal (year: 2021, volume: 2021, pages: 890-915), Publisher: Taylor & Francis
    Status:
    Published
    DOI:
    10.1080/03461238.2021.1902853 – link to the publication
  12. On the continuity of pickands constants

    Authors:
    Krzysztof Dębicki , Enkelejd Hashorva, Zbigniew Michna
    Academic press:
    Journal of Applied Probability (year: 2022, volume: 59 (1), pages: 187-201), Publisher: Cambridge University Press
    Status:
    Published
    DOI:
    10.1017/jpr.2021.42 – link to the publication
  13. Derivatives of sup-functionals of fractional Brownian motion evaluated at H=1/2

    Authors:
    Krzysztof Bisewski, Krzysztof Dębicki, Tomasz Rolski
    Academic press:
    Electronic Journal of Probability (year: 2022, volume: 27, pages: 12785), Publisher: The Institute of Mathematical Statistics and the Bernoulli Society
    Status:
    Published
    DOI:
    10.1214/22-EJP848 – link to the publication
  14. Exact asymptotics of component-wise extrema of two-dimensional Brownian motion

    Authors:
    K. Dębicki, L. Ji, T. Rolski
    Academic press:
    Extremes (year: 2020, volume: 23, pages: 569–602), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s10687-020-00387-y – link to the publication
  15. Pandemic-type failures in multivariate Brownian risk models

    Authors:
    Krzysztof Dębicki, Enkelejd Hashorva, Nikolai Kriukov
    Academic press:
    Extremes (year: 2022, volume: 25, pages: 46045), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s10687-021-00424-4 – link to the publication
  16. Proportional reinsurance for fractional Brownian risk model

    Authors:
    K. Kępczyński
    Academic press:
    Silesian Statistical Review (year: 2020, volume: 18, pages: 149-162), Publisher: Uniwersytet Ekonomiczny we Wrocławiu
    Status:
    Published
    DOI:
    10.15611/sps.2020.18.08 – link to the publication
  17. Extremes of vector-valued Gaussian processes

    Authors:
    K. Dębicki, E. Hashorva, L. Wang
    Academic press:
    Stochastic Processes and their Applications (year: 2020, volume: 130, pages: 5802-5837), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2020.04.008 – link to the publication

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Graphic design and implementation: Jakub Piotrowski