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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Markov jump processes and nonlocal operators

2011/03/B/ST1/00423

Keywords:

Markov processes stable processes transition density Green function hyperbolic spaces nonlocal operators fractional Laplacian Schrodinger operators

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 :

Politechnika Wrocławska, Wydział Podstawowych Problemów Techniki

woj. dolnośląskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Tadeusz Kulczycki 

Number of co-investigators in the project: 4

Call: OPUS 2 - announced on 2011-09-15

Amount awarded: 432 000 PLN

Project start date (Y-m-d): 2012-08-06

Project end date (Y-m-d): 2015-08-05

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

Project status: Project settled

Equipment purchased [PL]

  1. tablet biznesowy z oprogramowaniem i akcesoriami (w tym m.in. z klawiaturą).
  2. laptop z oprogramowaniem (4 szt.) (16 000 PLN)

Information in the final report

  • Publication in academic press/journals (12)
  1. Sharp estimates of Green function of hyperbolic Brownian motion
    Authors:
    K. Bogus, T. Byczkowski, J. Małecki
    Academic press:
    Studia Mathematica (rok: 2015, tom: 228, strony: 197-221), Wydawca: Instytut Matematyczny PAN
    Status:
    Published
    DOI:
    10.4064/sm228-3-1 - link to the publication
  2. Density and tails of unimodal convolution semigroups
    Authors:
    K. Bogdan, T. Grzywny, M. Ryznar
    Academic press:
    Journal of Functional Analysis (rok: 2014, tom: vol. 266, no. 6, strony: 3543–3571), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jfa.2014.01.007 - link to the publication
  3. Dirichlet heat kernel for unimodal Levy processes
    Authors:
    K. Bogdan, T. Grzywny, M. Ryznar
    Academic press:
    Stochastic Processes and their Applications (rok: 2014, tom: 124, strony: 3612-3650), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2014.06.001 - link to the publication
  4. Multiple solutions for Dirichlet nonlinear BVPs involving fractional Laplacian
    Authors:
    T. Kulczycki, R. Stańczy
    Academic press:
    Discrete and Continuous Dynamical Systems - Series B (DCDS-B) (rok: 2014, tom: 8, strony: 2581 - 2591), Wydawca: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/dcdsb.2014.19.2581 - link to the publication
  5. Exit time of a hyperbolic $\alpha$-stable process from a half-space or a ball
    Authors:
    M. Ryznar, T. Żak
    Academic press:
    Potential Analysis , Wydawca: Springer
    Status:
    Submitted
    DOI:
    brak - link to the publication
  6. First passage times for subordinate Brownian motions.
    Authors:
    M. Kwaśnicki, J. Małecki, M. Ryznar
    Academic press:
    Stochastic Processes and Applications (rok: 2013, tom: vol. 123, no. 5, strony: 1820–1850), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2013.01.011 - link to the publication
  7. Gradient Estimates of q-Harmonic Functions of Fractional Schrödinger Operator
    Authors:
    T. Kulczycki
    Academic press:
    Potential Analysis (rok: 2013, tom: Vol. 39, no. 1, strony: 69-98), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-012-9322-9 - link to the publication
  8. Mid-concavity of survival probability for isotropic Lévy processes
    Authors:
    T. Kulczycki
    Academic press:
    Electronic Communications in Probability , Wydawca: Institute of Mathematical Statistics (IMS) and the Bernoulli Society
    Status:
    Submitted
    DOI:
    brak - link to the publication
  9. Barriers, exit time and survival probability for unimodal Lévy processes
    Authors:
    K. Bogdan, T. Grzywny, M. Ryznar
    Academic press:
    Probability Theory Related Fields (rok: 2015, tom: 162(1), strony: 155-198), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00440-014-0568-6 - link to the publication
  10. Gradient estimates of harmonic functions and transition densities for Lévy processes
    Authors:
    T. Kulczycki, M. Ryznar
    Academic press:
    Transactions of the American Mathematical Society (rok: 2016, tom: 368(1), strony: 281-318), Wydawca: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/tran/6333 - link to the publication
  11. Extremal properties of one-dimensional Cauchy-type measures
    Authors:
    T. Byczkowski, T. Żak
    Academic press:
    Probability and Mathematical Statistics (rok: 2015, ), Wydawca: Kazimierz Urbanik Center for Probability and Mathematical Statistics
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication
  12. On concavity of solutions of the Dirichlet problem for the equation $(-\Delta)^{1/2} \vp = 1$ in convex planar regions
    Authors:
    T. Kulczycki
    Academic press:
    Journal of the European Mathematical Society , Wydawca: European Mathematical Society Publishing House
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication

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