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Structure, stability, and sensitivity analysis for Lévy-driven stochastic systems: the generalized coupling approach

2019/33/B/ST1/02923

Keywords:

Stochastic equation Lévy noise long memory coupling stability sensitivity

Descriptors:

  • ST1_013:

Panel:

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

Host institution :

Politechnika Wrocławska

woj. dolnośląskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

dr hab. Oleksii Kulyk 

Number of co-investigators in the project: 1

Call: OPUS 17 - announced on 2019-03-15

Amount awarded: 232 640 PLN

Project start date (Y-m-d): 2020-02-05

Project end date (Y-m-d): 2024-02-04

Project duration:: 48 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 (11)
  1. Support Theorem for Lévy-driven Stochastic Differential Equations
    Authors:
    Oleksii Kulyk
    Academic press:
    Journal of Theoretical Probability (rok: 2023, tom: 36, strony: 1720–1742), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10959-022-01223-8 - link to the publication
  2. Gradient formula for transition semigroup corresponding to stochastic equation driven by a system of independent L´evy processes
    Authors:
    Alexei M. Kulik, Szymon Peszat and Enrico Priola
    Academic press:
    Nonlinear Differential Equations and Applications (rok: 2023, tom: 30, strony: 45684), Wydawca: Birkhauser
    Status:
    Published
    DOI:
    10.1007/s00030-022-00810-2 - link to the publication
  3. Moment bounds for dissipative semimartingales with heavy jumps
    Authors:
    Alexei Kulik, Ilya Pavlyukevich
    Academic press:
    Stochastic Processes and their Applications (rok: 2021, tom: 141, strony: 274-308), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2021.07.004 - link to the publication
  4. On Regularization by a Small Noise of Multidimensional Odes with Non-Lipschitz Coefficients
    Authors:
    Alexei Kulik, Andrey Pilipenko
    Academic press:
    Ukrainian Mathematical Journal (rok: 2021, tom: 72, strony: 1445–1481)
    Status:
    Published
    DOI:
    10.1007/s11253-021-01865-7 - link to the publication
  5. Moment bounds for dissipative semimartingales with heavy jumps
    Authors:
    Alexei Kulik, Ilya Pavlyukevich
    Academic press:
    Stochastic Processes and their Applications (rok: 2021, tom: 141, strony: 274-308), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2021.07.004 - link to the publication
  6. On Regularization by a Small Noise of Multidimensional Odes with Non-Lipschitz Coefficients
    Authors:
    Alexei Kulik, Andrey Pilipenko
    Academic press:
    Ukrainian Mathematical Journal (rok: 2021, tom: 72, strony: 1445–1481)
    Status:
    Published
    DOI:
    10.1007/s11253-021-01865-7 - link to the publication
  7. Gradient formula for transition semigroup corresponding to stochastic equation driven by a system of independent L´evy processes
    Authors:
    Alexei M. Kulik, Szymon Peszat and Enrico Priola
    Academic press:
    Nonlinear Differential Equations and Applications (rok: 2023, tom: 30, strony: 45684), Wydawca: Birkhauser
    Status:
    Published
    DOI:
    10.1007/s00030-022-00810-2 - link to the publication
  8. On reflected diffusions in cones and cylinders
    Authors:
    Oleksii Kulyk, Andrey Pilipenko, Sylvie Roelly
    Academic press:
    Ukrains'kyi Matematychnyi Zhurnal (transl. in Ukrainian Mathematical Journal) (rok: 2023, tom: 75, strony: 1497-1521), Wydawca: Institute of Mathematics NAS of Ukraine
    Status:
    Published
    DOI:
    10.3842/umzh.v75i11.7418 - link to the publication
  9. On Regularization by a Small Noise of Multidimensional Odes with Non-Lipschitz Coefficients
    Authors:
    Alexei Kulik, Andrey Pilipenko
    Academic press:
    Ukrainian Mathematical Journal (rok: 2021, tom: 72, strony: 1445–1481)
    Status:
    Published
    DOI:
    10.1007/s11253-021-01865-7 - link to the publication
  10. Moment bounds for dissipative semimartingales with heavy jumps
    Authors:
    Alexei Kulik, Ilya Pavlyukevich
    Academic press:
    Stochastic Processes and their Applications (rok: 2021, tom: 141, strony: 274-308), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2021.07.004 - link to the publication
  11. Support Theorem for Lévy-driven Stochastic Differential Equations
    Authors:
    Oleksii Kulyk
    Academic press:
    Journal of Theoretical Probability (rok: 2023, tom: -, strony: -), Wydawca: Springer
    Status:
    Accepted for publication
    DOI:
    10.1007/s10959-022-01223-8 - link to the publication

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