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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Levy and Markov processes on Euclidean and hyperbolic spaces

2015/17/B/ST1/01043

Keywords:

Levy process heat kernel Levy measure hitting distribution exit time Green function selfsimilar Markov process dual process subordinate Brownian motion hyperbolic Brownian motion hyperbolic stable motion

Descriptors:

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

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

woj. 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 (Y-m-d): 2016-03-17

Project end date (Y-m-d): 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 (5 000 PLN)
  2. Laptop (10 000 PLN)

Information in the final report

  • Publication in academic press/journals (13)
  1. Heat content for convolution semigroups
    Authors:
    Wojciech Cygan, Tomasz Grzywny
    Academic press:
    Journal of Mathematical Analysis and Applications (rok: 2017, tom: 446, strony: 1393–1414), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2016.09.051 - link to the publication
  2. Hitting probabilities for Lévy processes on the real line
    Authors:
    Tomasz Grzywny, Łukasz Leżaj, Maciej Miiśta,
    Academic press:
    Stochastic Processes and their Applications , Wydawca: Elsevier
    Status:
    Submitted
    DOI:
    brak - link to the publication
  3. Asymptotic Behaviour and Estimates of Slowly Varying Convolution Semigroups
    Authors:
    Tomasz Grzywny, Michał Ryznar, Bartosz Trojan
    Academic press:
    International Mathematics Research Notices (rok: 2019, tom: 2019/23, strony: 7193–7258), Wydawca: Oxford University Press
    Status:
    Published
    DOI:
    10.1093/imrn/rnx324 - link to the publication
  4. Gradient estimates of Dirichlet heat kernels for unimodal Lévy processes
    Authors:
    Tadeusz Kulczycki, Michał Ryznar
    Academic press:
    Mathematische Nachrichten (rok: 2018, tom: 291, Issue 2-3, strony: 374–397), Wydawca: WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
    Status:
    Published
    DOI:
    10.1002/mana.201600443 - link to the publication
  5. Space and time inversions of stochastic processes and Kelvin transform
    Authors:
    Larbi Alili, Loic Chaumont, Piotr Graczyk, Tomasz Żak
    Academic press:
    Mathematische Nachrichten (rok: 2019, tom: 292, strony: 252–272), Wydawca: WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
    Status:
    Published
    DOI:
    10.1002/mana.201700152 - link to the publication
  6. 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 (rok: 2017, tom: 22, strony: 1–18), Wydawca: Institute of Mathematical Statistics, Bernoulli Society.
    Status:
    Published
    DOI:
    10.1214/17-EJP33 - link to the publication
  7. 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 (rok: 2020, tom: 130/12, strony: 7185-7217), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2020.07.011 - 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 (rok: 2020, tom: online, strony: 18994), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-020-09850-8 - link to the publication
  9. First exit times from a bounded interval for Lévy processes
    Authors:
    Tomasz Grzywny
    Academic press:
    Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques , Wydawca: Association des Publications de l'Institut Henri Poincaré
    Status:
    Submitted
    DOI:
    btrak - link to the publication
  10. Hyperbolic Green function estimates
    Authors:
    Michał Ryznar, Grzegorz Serafin, Tomasz Żak
    Academic press:
    Potential Analysis (rok: 2020, tom: online, strony: 45316), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-020-09837-5 - link to the publication
  11. 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 (rok: 2018, tom: 15, strony: 1335-1375), Wydawca: Instituto Nacional de Matematica Pura e Aplicada
    Status:
    Published
    DOI:
    10.30757/ALEA.v15-50 - link to the publication
  12. Transition density of a hyperbolic Bessel proces
    Authors:
    Andrzej Pyć, Tomasz Żak
    Academic press:
    Electronic Communications in Probability (rok: 2016, tom: 21, strony: 1–10), Wydawca: Institute of Mathematical Statistics, Bernoulli Society
    Status:
    Published
    DOI:
    10.1214/16-ECP8 - link to the publication
  13. BORELL AND LANDAU-SHEPP INEQUALITIES FOR CAUCHY-TYPEMEASURES
    Authors:
    Tomasz Byczkowski, Tomasz Żak
    Academic press:
    Probability and Mathematical Statistics , Wydawca: Wydawnictwo Uniwersytetu Wrocławskiego Sp. z o.o. Uniwersytet Wrocławski
    Status:
    Accepted for publication
    DOI:
    10.19195/0208-4147.0.0.0 - link to the publication

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