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Excursions of vector-valued Gaussian stochastic processes: exact asymptotics

2018/31/B/ST1/00370

Keywords:

exit probability supremum sojourn time Gaussian process

Descriptors:

  • ST1_13: Probability and statistics

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

woj. dolnośląskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Krzysztof 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 (Y-m-d): 2019-07-24

Project end date (Y-m-d): 2024-07-23

Project duration:: 36 months (the same as in the proposal)

Project status: Project completed

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 (14)
  1. Derivative of the expected supremum of fractional Brownian motion at H=1
    Authors:
    Krzysztof Bisewski, Krzysztof Dȩbicki, Tomasz Rolski
    Academic press:
    Queueing Systems (rok: 2022, tom: 102, strony: 53-68), Wydawca: Springer US
    Status:
    Published
    DOI:
    10.1007/s11134-022-09859-3 - link to the publication
  2. Simultaneous ruin probability for multivariate Gaussian risk model
    Authors:
    Bisewski Krzysztof, Dębicki Krzysztof, Kriukov Nikolai
    Academic press:
    Stochastic Processes and their Applications (rok: 2023, tom: 160, strony: 386-408), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1016/j.spa.2023.03.002 - link to the publication
  3. 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. (rok: 2023, tom: 20, strony: 249–289), Wydawca: IMS
    Status:
    Published
    DOI:
    10.30757/ALEA.v20-10 - link to the publication
  4. Sojourns of stationary Gaussian processes over a random interval
    Authors:
    Dębicki Krzysztof, Peng Xiaofan
    Academic press:
    ALEA-Latin Am. J. Probab. Math. (rok: 2023, tom: 20, strony: 1017–1039), Wydawca: IMS
    Status:
    Published
    DOI:
    10.30757/ALEA.v20-37 - link to the publication
  5. Bounds for expected supremum of fractional Brownian motion with drift
    Authors:
    Krzysztof Bisewski, Krzysztof Dębicki, Michel Mandjes
    Academic press:
    Journal of Applied Probability (rok: 2021, tom: 58, strony: 411-427), Wydawca: Cambridge University Press
    Status:
    Published
    DOI:
    10.1017/jpr.2020.98 - link to the publication
  6. Pandemic-type failures in multivariate Brownian risk models
    Authors:
    Krzysztof Dębicki, Enkelejd Hashorva, Nikolai Kriukov
    Academic press:
    Extremes (rok: 2022, tom: 25, strony: 45314), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10687-021-00424-4 - link to the publication
  7. 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 (rok: 2022, tom: 27, strony: 12785), Wydawca: The Institute of Mathematical Statistics and the Bernoulli Society
    Status:
    Published
    DOI:
    10.1214/22-EJP848 - link to the publication
  8. Finite-time ruin probability for correlated Brownian motions
    Authors:
    Krzysztof Dębicki, Enkelejd Hashorva, Konrad Krystecki
    Academic press:
    Scandinavian Actuarial Journal (rok: 2021, tom: 2021, strony: 890-915), Wydawca: Taylor & Francis
    Status:
    Published
    DOI:
    10.1080/03461238.2021.1902853 - link to the publication
  9. On the continuity of pickands constants
    Authors:
    Krzysztof Dębicki , Enkelejd Hashorva, Zbigniew Michna
    Academic press:
    Journal of Applied Probability (rok: 2022, tom: 59 (1), strony: 187-201), Wydawca: Cambridge University Press
    Status:
    Published
    DOI:
    10.1017/jpr.2021.42 - link to the publication
  10. Running supremum of Brownian motion in dimension 2: exact and asymptotic results
    Authors:
    Krzysztof Kępczyński
    Academic press:
    Stochastic Modles (rok: 2022, tom: 38, strony: 116-129), Wydawca: Taylor & Francis
    Status:
    Published
    DOI:
    10.1080/15326349.2021.1982395 - link to the publication
  11. Proportional reinsurance for fractional Brownian risk model
    Authors:
    K. Kępczyński
    Academic press:
    Silesian Statistical Review (rok: 2020, tom: 18, strony: ), Wydawca: Uniwersytet Ekonomiczny we Wrocławiu
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication
  12. Exact asymptotics of component-wise extrema of two-dimensional Brownian motion
    Authors:
    K. Dębicki, L. Ji, T. Rolski
    Academic press:
    Extremes (rok: 2020, tom: 23, strony: 569–602), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10687-020-00387-y - link to the publication
  13. Sojourns of fractional Brownian motion queues: transient asymptotics
    Authors:
    Dębicki Krzysztof, Hashorva Enkelejd, Liu Peng
    Academic press:
    Queueing Systems (rok: 2023, tom: 105, strony: 139-170), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11134-023-09890-y - link to the publication
  14. Extremes of vector-valued Gaussian processes
    Authors:
    K. Dębicki, E. Hashorva, L. Wang
    Academic press:
    Stochastic Processes and their Applications (rok: 2020, tom: 130, strony: 5802-5837), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2020.04.008 - link to the publication

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