Applications of stochastic analysis

2012/07/B/ST1/03356

Keywords

Descriptors

  • ST1_13: Rachunek prawdopodobieństwa i statystyka matematyczna
  • ST1_11: Równania różniczkowe cząstkowe
  • ST1_9: Algebry operatorowe i analiza funkcjonalna

Panel

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

Host institution

Instytut Matematyczny Polskiej Akademii Nauk

Voivodeship: mazowieckie

Other projects carried out by the institution »

Principal investigator (from the host institution)

prof. Krzysztof Michał Bogdan

Number of co-investigators in the project: 5

Call

OPUS 4 – announced on 2012-09-15

Amount awarded
392 060 PLN
Project start date
2013-07-08
Project end date
2016-07-07
Project duration
36 months (the same as in the proposal)
Project status
Project settled

Equipment purchased [PL]

  1. laptopy. Cost: 9 600 PLN

Information in the final report

Publication in academic press/journals (25)

  1. Small time sharp bounds for kernels of convolution semigroups

    Authors:
    Kaleta, Kamil; Sztonyk, Paweł
    Academic press:
    J. Anal. Math. (year: 2017, volume: 172, pages: 355-394), Publisher: SIAM
    Status:
    Published
    DOI:
    10.1007/s11854-017-0023-6 – link to the publication
  2. Principal eigenvalue of the fractional Laplacian with a large incompressible drift

    Authors:
    Bogdan, Krzysztof; Komorowski, Tomasz
    Academic press:
    NoDEA Nonlinear Differential Equations Appl. (year: 2014, volume: 21, pages: 541-566), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00030-013-0257-7 – link to the publication
  3. Dirichlet heat kernel for unimodal Lévy processes

    Authors:
    Bogdan, Krzysztof; Grzywny, Tomasz; Ryznar, Michał
    Academic press:
    Stochastic Process. Appl. (year: 2014, volume: 124 (11), pages: 3612-3650), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2014.06.001 – link to the publication
  4. Estimates of transition densities and their derivatives for jump Lévy processes

    Authors:
    Kaleta, Kamil; Sztonyk, Paweł
    Academic press:
    J. Math. Anal. Appl. (year: 2015, volume: 431 (1), pages: 260-282), Publisher: Elsevier, Inc.
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2015.05.061 – link to the publication
  5. Martin kernel for fractional Laplacian in narrow cones

    Authors:
    Bogdan, Krzysztof; Siudeja, Bartłomiej; Stós, Andrzej
    Academic press:
    Potential Anal. (year: 2015, volume: 42, pages: 839-859), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-014-9459-9 – link to the publication
  6. Barriers, exit time and survival probability for unimodal Lévy processes

    Authors:
    Bogdan, Krzysztof; Grzywny, Tomasz; Ryznar, Michał
    Academic press:
    Probab. Theory Relat. Fields (year: 2015, volume: 162, pages: 155–198), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00440-014-0568-6 – link to the publication
  7. Characterizations for fractional Hardy inequality

    Authors:
    Dyda, Bartłomiej; Vähäkangas, Antti V.
    Academic press:
    Adv. Calc. Var. (year: 2015, volume: 8 (2), pages: 173-182), Publisher: De Gruyter
    Status:
    Published
    DOI:
    10.1515/acv-2013-0019 – link to the publication
  8. Upper estimates of transition densities for stable-dominated semigroups

    Authors:
    Kaleta, Kamil; Sztonyk, Paweł
    Academic press:
    J. Evol. Equ. (year: 2013, volume: 13(3), pages: 633--650), Publisher: Birkhäuser Basel
    Status:
    Published
    DOI:
    10.1007/s00028-013-0194-2 – link to the publication
  9. Majorization, 4G Theorem and Schrödinger perturbations

    Authors:
    Bogdan, Krzysztof; Butko, Yana; Szczypkowski, Karol
    Academic press:
    Journal of Evolution Equations (year: 2016, volume: 16, pages: 241-260), Publisher: Birkhäuser Verlag
    Status:
    Published
    DOI:
    10.1007/s00028-015-0301-7 – link to the publication
  10. Density and tails of unimodal convolution semigroups

    Authors:
    Bogdan, Krzysztof; Grzywny, Tomasz; Ryznar, Michał
    Academic press:
    J. Funct. Anal. (year: 2014, volume: 266 (6), pages: 3543-3571), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jfa.2014.01.007 – link to the publication
  11. A framework for fractional Hardy inequalities

    Authors:
    Dyda, Bartłomiej; Vähäkangas, Antti V.
    Academic press:
    Ann. Acad. Sci. Fenn. Math. (year: 2014, volume: 39, pages: 675-689), Publisher: Finnish Academy of Science and Letters
    Status:
    Published
    DOI:
    10.5186/aasfm.2014.3943 – link to the publication
  12. Generalized tight p-frames and spectral bounds for Laplace-like operators

    Authors:
    Siudeja, Bartłomiej
    Academic press:
    Applied and Computational Harmonic Analysis (year: 2017, volume: 42, pages: 167–198), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.acha.2015.08.001 – link to the publication
  13. Eigenvalues of the fractional Laplace operator in the unit ball

    Authors:
    Bartłomiej Dyda, Alexey Kuznetsov, Mateusz Kwaśnicki
    Academic press:
    J. London Math. Soc. (year: 2017, volume: 95, pages: 500-518), Publisher: Oxford University Press
    Status:
    Published
    DOI:
    10.1112/jlms.12024 – link to the publication
  14. Steklov Eigenvalues and Quasiconformal Maps of Simply Connected Planar Domains

    Authors:
    Girouard, A.; Laugesen, R. S.; Siudeja, B. A.
    Academic press:
    Arch Rational Mech Anal (year: 2016, volume: 219, pages: 903--936), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00205-015-0912-8 – link to the publication
  15. Estimates of densities for Lévy processes with lower intensity of large jumps

    Authors:
    Sztonyk, Paweł
    Academic press:
    Math. Nachr. (year: 2016, volume: bd, pages: bd), Publisher: Wiley-VCH Verlag
    Status:
    Published
    DOI:
    10.1002/mana201500189 – link to the publication
  16. Hardy–Stein identities and square functions for semigroups

    Authors:
    Bogdan, Krzysztof; Banuelos, Rodrigo; Luks, Tomasz
    Academic press:
    J. London Math. Soc. (year: 2016, volume: 94, pages: 462-478), Publisher: London Mathematical Society
    Status:
    Published
    DOI:
    10.1112/jlms/jdw042 – link to the publication
  17. Trace estimates for unimodal Lévy processes

    Authors:
    Bogdan, Krzysztof; Siudeja, Bartłomiej
    Academic press:
    J. Evol. Equ. (year: 2016, volume: 16, pages: 857–876), Publisher: Birkhäuser Verlag
    Status:
    Published
    DOI:
    10.1007/s00028-016-0322-x – link to the publication
  18. The shape of the fundamental sloshing mode in axisymmetric containers

    Authors:
    Kulczycki, Tadeusz; Kwasnicki, Mateusz; Siudeja, Bartlomiej
    Academic press:
    J. Engineering Math. (year: 2016, volume: 99, pages: 157–183), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s10665-015-9826-6 – link to the publication
  19. On improved fractional Sobolev-Poincaré inequalities

    Authors:
    Dyda, Bartłomiej; Ihnatsyeva, Lizaveta; Vähäkangas, Antti V.
    Academic press:
    Arkiv för Matematik (year: 2016, volume: 24, pages: 437-454), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s11512-015-0227-x – link to the publication
  20. Hardy Inequalities and non-explosion Results for Semigroups

    Authors:
    Bogdan, Krzysztof; Dyda, Bartłomiej; Kim, Panki
    Academic press:
    Potential Anal. (year: 2016, volume: 44 (2), pages: 229-247), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-015-9507-0 – link to the publication
  21. Hot spots conjecture for a class of acute triangles

    Authors:
    Siudeja, Bartłomiej
    Academic press:
    Math. Z. (year: 2015, volume: 280 (3), pages: 783-806), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00209-015-1448-1 – link to the publication
  22. The Schur-Horn theorem for unbounded operators with discrete spectrum

    Authors:
    Bownik,Marcin; Jasper, John; Siudeja, Bartłomiej
    Academic press:
    B. London Math Soc (year: 2017, volume: 49, pages: 148-164), Publisher: Oxford University Press
    Status:
    Published
    DOI:
    10.1112/blms.12013 – link to the publication
  23. Magnetic spectral bounds on starlike plane domains

    Authors:
    Laugesen, Richard S.; Siudeja, Bartlomiej
    Academic press:
    ESAIM Control Optim. Calc. Var. (year: 2015, volume: 21 (3), pages: 670-689), Publisher: EDP
    Status:
    Published
    DOI:
    10.1051/cocv/2014043 – link to the publication
  24. Fractional Laplace operator and Meijer G-function

    Authors:
    Dyda, Bartłomiej; Kuznetsov, Alexey; Kwaśnicki, Mateusz
    Academic press:
    Constructive Approximation (year: 2017, volume: 45, pages: 427–448), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00365-016-9336-4 – link to the publication
  25. Regularity estimates for elliptic nonlocal operators

    Authors:
    Bartłomiej Dyda, Moritz Kassmann
    Status:
    Accepted for publication

Book publications / chapters in book publications (1)

  1. Levy systems and moment formulas for mixed Poisson integrals

    Authors:
    Bogdan, Krzysztof; Rosiński, Jan; Serafin, Grzegorz; Wojciechowski
    Book:
    Stochastic Analysis and its Applications, A Festschrift in Honor of Rodrigo Banuelos, Progress in Probability (year: 2017, volume: 72, pages: 139-164), Publisher: Springer
    Status:
    Published

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Graphic design and implementation: Jakub Piotrowski