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Levy and Markov processes on Euclidean and hyperbolic spaces

2015/17/B/ST1/01043

Keywords

Descriptors

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

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 Matematyki

Voivodeship: dolnośląskie

Other projects carried out by the institution »

Principal investigator (from the host institution)

prof. Michał Ryznar

Number of co-investigators in the project: 4

Call

OPUS 9 – announced on 2015-03-16

Amount awarded
346 200 PLN
Project start date
2016-03-17
Project end date
2019-09-16
Project duration
42 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.

Equipment purchased [PL]

  1. Laptop. Cost: 5 000 PLN
  2. Laptop. Cost: 10 000 PLN

Information in the final report

Publication in academic press/journals (11)

  1. Semigroup properties of solutions of SDEs driven by Lévy processes with independent coordinates

    Authors:
    Tadeusz Kulczycki , Michał Ryznar
    Academic press:
    Stochastic Processes and their Applications (year: 2020, volume: 130/12, pages: 7185-7217), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2020.07.011 – link to the publication

  2. Hyperbolic Green function estimates

    Authors:
    Michał Ryznar, Grzegorz Serafin, Tomasz Żak
    Academic press:
    Potential Analysis (year: 2020, volume: online, pages: 46047), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-020-09837-5 – link to the publication

  3. Space and time inversions of stochastic processes and Kelvin transform

    Authors:
    Larbi Alili, Loic Chaumont, Piotr Graczyk, Tomasz Żak
    Academic press:
    Mathematische Nachrichten (year: 2019, volume: 292, pages: 252–272), Publisher: WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
    Status:
    Published
    DOI:
    10.1002/mana.201700152 – link to the publication

  4. Heat content for convolution semigroups

    Authors:
    Wojciech Cygan, Tomasz Grzywny
    Academic press:
    Journal of Mathematical Analysis and Applications (year: 2017, volume: 446, pages: 1393–1414), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2016.09.051 – link to the publication

  5. Inversions, duality and Doob h-transforms for self-similar Markov processes

    Authors:
    Larbi Alili, Loic Chaumont, Piotr Graczyk, Tomasz Żak
    Academic press:
    Electronic Journal of Probability (year: 2017, volume: 22, pages: 1–18), Publisher: Institute of Mathematical Statistics, Bernoulli Society.
    Status:
    Published
    DOI:
    10.1214/17-EJP33 – link to the publication

  6. Transition density of a hyperbolic Bessel proces

    Authors:
    Andrzej Pyć, Tomasz Żak
    Academic press:
    Electronic Communications in Probability (year: 2016, volume: 21, pages: 1–10), Publisher: Institute of Mathematical Statistics, Bernoulli Society
    Status:
    Published
    DOI:
    10.1214/16-ECP8 – link to the publication

  7. Gradient estimates of Dirichlet heat kernels for unimodal Lévy processes

    Authors:
    Tadeusz Kulczycki, Michał Ryznar
    Academic press:
    Mathematische Nachrichten (year: 2018, volume: 291, Issue 2-3, pages: 374–397), Publisher: WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
    Status:
    Published
    DOI:
    10.1002/mana.201600443 – link to the publication

  8. Strong Feller property for SDEs driven by multiplicative cylindrical stable noise

    Authors:
    T. Kulczycki, M. Ryznar, P. Sztonyk
    Academic press:
    Potential Analysis (year: 2020, volume: online, pages: 18994), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-020-09850-8 – link to the publication

  9. Transition density estimates for diagonal systems of SDEs driven by cylindrical α-stable processes

    Authors:
    Tadeusz Kulczycki, Michal Ryznar
    Academic press:
    ALEA/Latin American Journal of Probability and Mathematical Statistics (year: 2018, volume: 15, pages: 1335-1375), Publisher: Instituto Nacional de Matematica Pura e Aplicada
    Status:
    Published
    DOI:
    10.30757/ALEA.v15-50 – link to the publication

  10. Asymptotic Behaviour and Estimates of Slowly Varying Convolution Semigroups

    Authors:
    Tomasz Grzywny, Michał Ryznar, Bartosz Trojan
    Academic press:
    International Mathematics Research Notices (year: 2019, volume: 2019/23, pages: 7193–7258), Publisher: Oxford University Press
    Status:
    Published
    DOI:
    10.1093/imrn/rnx324 – link to the publication

  11. BORELL AND LANDAU-SHEPP INEQUALITIES FOR CAUCHY-TYPEMEASURES

    Authors:
    Tomasz Byczkowski, Tomasz Żak
    Status:
    Accepted for publication

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