Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

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Applications of stochastic analysis

2012/07/B/ST1/03356

Keywords:

eigenvalue semigroup Markov process martingale quadratic form fractional Laplacian

Descriptors:

  • ST1_13: Probability and statistics
  • ST1_11: Partial differential equations
  • ST1_9: Operator algebras and functional analysis

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 PAN

woj. mazowieckie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Krzysztof 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 (Y-m-d): 2013-07-08

Project end date (Y-m-d): 2016-07-07

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

Project status: Project settled

Equipment purchased [PL]

  1. laptopy (9 600 PLN)

Information in the final report

  • Publication in academic press/journals (25)
  • Book publications / chapters in book publications (1)
  1. Trace estimates for unimodal Lévy processes
    Authors:
    Bogdan, Krzysztof; Siudeja, Bartłomiej
    Academic press:
    J. Evol. Equ. (rok: 2016, tom: 16, strony: 857–876), Wydawca: Birkhäuser Verlag
    Status:
    Published
    DOI:
    10.1007/s00028-016-0322-x - link to the publication
  2. Barriers, exit time and survival probability for unimodal Lévy processes
    Authors:
    Bogdan, Krzysztof; Grzywny, Tomasz; Ryznar, Michał
    Academic press:
    Probab. Theory Relat. Fields (rok: 2015, tom: 162, strony: 155–198), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00440-014-0568-6 - link to the publication
  3. Characterizations for fractional Hardy inequality
    Authors:
    Dyda, Bartłomiej; Vähäkangas, Antti V.
    Academic press:
    Adv. Calc. Var. (rok: 2015, tom: 8 (2), strony: 173-182), Wydawca: De Gruyter
    Status:
    Published
    DOI:
    10.1515/acv-2013-0019 - link to the publication
  4. Estimates of densities for Lévy processes with lower intensity of large jumps
    Authors:
    Sztonyk, Paweł
    Academic press:
    Math. Nachr. (rok: 2016, tom: bd, strony: bd), Wydawca: Wiley-VCH Verlag
    Status:
    Published
    DOI:
    10.1002/mana201500189 - link to the publication
  5. Estimates of transition densities and their derivatives for jump Lévy processes
    Authors:
    Kaleta, Kamil; Sztonyk, Paweł
    Academic press:
    J. Math. Anal. Appl. (rok: 2015, tom: 431 (1), strony: 260-282), Wydawca: Elsevier, Inc.
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2015.05.061 - link to the publication
  6. Hardy Inequalities and non-explosion Results for Semigroups
    Authors:
    Bogdan, Krzysztof; Dyda, Bartłomiej; Kim, Panki
    Academic press:
    Potential Anal. (rok: 2016, tom: 44 (2), strony: 229-247), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-015-9507-0 - link to the publication
  7. Hot spots conjecture for a class of acute triangles
    Authors:
    Siudeja, Bartłomiej
    Academic press:
    Math. Z. (rok: 2015, tom: 280 (3), strony: 783-806), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00209-015-1448-1 - link to the publication
  8. 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 (rok: 2016, tom: 219, strony: 903--936), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00205-015-0912-8 - link to the publication
  9. Regularity estimates for elliptic nonlocal operators
    Authors:
    Bartłomiej Dyda, Moritz Kassmann
    Academic press:
    Analysis & PDE , Wydawca: Mathematical Sciences Publishers
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication
  10. Magnetic spectral bounds on starlike plane domains
    Authors:
    Laugesen, Richard S.; Siudeja, Bartlomiej
    Academic press:
    ESAIM Control Optim. Calc. Var. (rok: 2015, tom: 21 (3), strony: 670-689), Wydawca: EDP
    Status:
    Published
    DOI:
    10.1051/cocv/2014043 - link to the publication
  11. Martin kernel for fractional Laplacian in narrow cones
    Authors:
    Bogdan, Krzysztof; Siudeja, Bartłomiej; Stós, Andrzej
    Academic press:
    Potential Anal. (rok: 2015, tom: 42, strony: 839-859), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-014-9459-9 - link to the publication
  12. On improved fractional Sobolev-Poincaré inequalities
    Authors:
    Dyda, Bartłomiej; Ihnatsyeva, Lizaveta; Vähäkangas, Antti V.
    Academic press:
    Arkiv för Matematik (rok: 2016, tom: 24, strony: 437-454), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11512-015-0227-x - link to the publication
  13. Principal eigenvalue of the fractional Laplacian with a large incompressible drift
    Authors:
    Bogdan, Krzysztof; Komorowski, Tomasz
    Academic press:
    NoDEA Nonlinear Differential Equations Appl. (rok: 2014, tom: 21, strony: 541-566), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00030-013-0257-7 - link to the publication
  14. Upper estimates of transition densities for stable-dominated semigroups
    Authors:
    Kaleta, Kamil; Sztonyk, Paweł
    Academic press:
    J. Evol. Equ. (rok: 2013, tom: 13(3), strony: 633--650), Wydawca: Birkhäuser Basel
    Status:
    Published
    DOI:
    10.1007/s00028-013-0194-2 - link to the publication
  15. A framework for fractional Hardy inequalities
    Authors:
    Dyda, Bartłomiej; Vähäkangas, Antti V.
    Academic press:
    Ann. Acad. Sci. Fenn. Math. (rok: 2014, tom: 39, strony: 675-689), Wydawca: Finnish Academy of Science and Letters
    Status:
    Published
    DOI:
    10.5186/aasfm.2014.3943 - link to the publication
  16. Dirichlet heat kernel for unimodal Lévy processes
    Authors:
    Bogdan, Krzysztof; Grzywny, Tomasz; Ryznar, Michał
    Academic press:
    Stochastic Process. Appl. (rok: 2014, tom: 124 (11), strony: 3612-3650), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2014.06.001 - link to the publication
  17. Eigenvalues of the fractional Laplace operator in the unit ball
    Authors:
    Bartłomiej Dyda, Alexey Kuznetsov, Mateusz Kwaśnicki
    Academic press:
    J. London Math. Soc. (rok: 2017, tom: 95, strony: 500-518), Wydawca: Oxford University Press
    Status:
    Published
    DOI:
    10.1112/jlms.12024 - link to the publication
  18. Fractional Laplace operator and Meijer G-function
    Authors:
    Dyda, Bartłomiej; Kuznetsov, Alexey; Kwaśnicki, Mateusz
    Academic press:
    Constructive Approximation (rok: 2017, tom: 45, strony: 427–448), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00365-016-9336-4 - link to the publication
  19. The Schur-Horn theorem for unbounded operators with discrete spectrum
    Authors:
    Bownik,Marcin; Jasper, John; Siudeja, Bartłomiej
    Academic press:
    B. London Math Soc (rok: 2017, tom: 49, strony: 148-164), Wydawca: Oxford University Press
    Status:
    Published
    DOI:
    10.1112/blms.12013 - link to the publication
  20. The shape of the fundamental sloshing mode in axisymmetric containers
    Authors:
    Kulczycki, Tadeusz; Kwasnicki, Mateusz; Siudeja, Bartlomiej
    Academic press:
    J. Engineering Math. (rok: 2016, tom: 99, strony: 157–183), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10665-015-9826-6 - link to the publication
  21. Density and tails of unimodal convolution semigroups
    Authors:
    Bogdan, Krzysztof; Grzywny, Tomasz; Ryznar, Michał
    Academic press:
    J. Funct. Anal. (rok: 2014, tom: 266 (6), strony: 3543-3571), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jfa.2014.01.007 - link to the publication
  22. Generalized tight p-frames and spectral bounds for Laplace-like operators
    Authors:
    Siudeja, Bartłomiej
    Academic press:
    Applied and Computational Harmonic Analysis (rok: 2017, tom: 42, strony: 167–198), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.acha.2015.08.001 - link to the publication
  23. Hardy–Stein identities and square functions for semigroups
    Authors:
    Bogdan, Krzysztof; Banuelos, Rodrigo; Luks, Tomasz
    Academic press:
    J. London Math. Soc. (rok: 2016, tom: 94, strony: 462-478), Wydawca: London Mathematical Society
    Status:
    Published
    DOI:
    10.1112/jlms/jdw042 - link to the publication
  24. Majorization, 4G Theorem and Schrödinger perturbations
    Authors:
    Bogdan, Krzysztof; Butko, Yana; Szczypkowski, Karol
    Academic press:
    Journal of Evolution Equations (rok: 2016, tom: 16, strony: 241-260), Wydawca: Birkhäuser Verlag
    Status:
    Published
    DOI:
    10.1007/s00028-015-0301-7 - link to the publication
  25. Small time sharp bounds for kernels of convolution semigroups
    Authors:
    Kaleta, Kamil; Sztonyk, Paweł
    Academic press:
    J. Anal. Math. (rok: 2017, tom: 172, strony: 355-394), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1007/s11854-017-0023-6 - link to the publication
  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 (rok: 2017, tom: 72, strony: 139-164), Wydawca: Springer
    Status:
    Published
    DOI:
    link to the publication

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