Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

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Probabilistic, numerical and statistical analysis of sub- and superdiffusion processes

2019/34/E/ST1/00360

Keywords:

subdiffusion superdiffusion fractional differential eqation approximation scheme continuous time random walk limit theorem functional convergence Skorochod topology statistical inference estimation

Descriptors:

  • ST1_13: Probability and statistics
  • ST1_17: Applied mathematics
  • ST3_15: Statistical physics of condensed matter, phase transitions, noise and fluctuations, etc.

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.

Other projects carried out by the institution 

Principal investigator (from the host institution):

dr hab. Marcin Magdziarz 

Number of co-investigators in the project: 4

Call: SONATA BIS 9 - announced on 2019-06-17

Amount awarded: 576 900 PLN

Project start date (Y-m-d): 2020-03-30

Project end date (Y-m-d): 2023-09-29

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.

Information in the final report

  • Publication in academic press/journals (34)
  1. Tempered processes in modelling of single-particle tracking experiments
    Authors:
    Krzysztof Burnecki, Aleksandra Rogalska
    Academic press:
    Mathematica Applicanda (rok: 2023, ), Wydawca: PTM
    Status:
    Submitted
  2. A compressed sensing approach to interpolation of fractional Brownian trajectories for a single particle tracking experiment
    Authors:
    Monika Muszkieta, Joanna Janczura
    Academic press:
    Applied Mathematics and Computation (rok: 2023, tom: 446, strony: 127900), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.amc.2023.127900 - link to the publication
  3. A tempered subdiffusive Black-Scholes model
    Authors:
    Grzegorz Krzyżanowski, Marcin Magdziarz
    Academic press:
    Fractional Calculus and Applied Analysis (rok: 2022, ), Wydawca: Walter de Gruyter
    Status:
    Submitted
  4. Classification of particle trajectories in living cells: Machine learning versus statistical testing hypothesis for fractional anomalous diffusion
    Authors:
    Joanna Janczura, Patrycja Kowalek, Hanna Loch-Olszewska, Janusz Szwabiński, Aleksander Weron
    Academic press:
    PHYSICAL REVIEW E (rok: 2020, tom: 102, strony: 32402), Wydawca: APS
    Status:
    Published
    DOI:
    10.1103/PhysRevE.102.032402 - link to the publication
  5. Zero Black-Derman-Toy Interest Rate Model
    Authors:
    Grzegorz Krzyżanowski, Ernesto Mordecki, Andrés Sosa
    Academic press:
    The Journal of Fixed Income (rok: 2022, tom: 31(3), strony: 93-111), Wydawca: PMR
    Status:
    Published
    DOI:
    10.3905/jfi.2021.1.122 - link to the publication
  6. Identifying heterogeneous diffusion states in the cytoplasm by a hidden Markov model
    Authors:
    Joanna Janczura, Michał Balcerek, Krzysztof Burnecki, Adal Sabri, Matthias Weiss, Diego Krapf
    Academic press:
    New Journal of Physics (rok: 2021, tom: 23, strony: 53018), Wydawca: IOP
    Status:
    Published
    DOI:
    10.1088/1367-2630/abf204 - link to the publication
  7. Classification of random trajectories based on the fractional Lévy stable motion
    Authors:
    Joanna Janczura, Krzysztof Burnecki, Monika Muszkieta, Aleksander Stanislavsky, Aleksander Weron
    Academic press:
    Chaos, Solitons and Fractals (rok: 2022, tom: 154, strony: 111606), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.chaos.2021.111606 - link to the publication
  8. Parameter estimation of the fractional Ornstein–Uhlenbeck process based on quadratic variation
    Authors:
    Joanna Janczura, Marcin Magdziarz, Ralf Metzler
    Academic press:
    Chaos (rok: 2023, tom: 33, strony: 103125), Wydawca: AIP
    Status:
    Published
    DOI:
    10.1063/5.0158843 - link to the publication
  9. Simulation and tracking of fractional particles motion. From microscopy video to statistical analysis. A Brownian bridge approach
    Authors:
    Monika Muszkieta, Joanna Janczura , Aleksander Weron
    Academic press:
    Applied Mathematics and Computation (rok: 2021, tom: 396, strony: 125902), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.amc.2020.125902 - link to the publication
  10. A compressed sensing approach to interpolation of fractional Brownian trajectories for a single particle tracking experiment
    Authors:
    Monika Muszkieta, Joanna Janczura
    Academic press:
    Applied Mathematics and Computation (rok: 2023, tom: 446, strony: 127900), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.amc.2023.127900 - link to the publication
  11. Classification of random trajectories based on the fractional Lévy stable motion
    Authors:
    Joanna Janczura, Krzysztof Burnecki, Monika Muszkieta, Aleksander Stanislavsky, Aleksander Weron
    Academic press:
    Chaos, Solitons and Fractals (rok: 2022, tom: 154, strony: 111606), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.chaos.2021.111606 - link to the publication
  12. Identifying heterogeneous diffusion states in the cytoplasm by a hidden Markov model
    Authors:
    Joanna Janczura, Michał Balcerek, Krzysztof Burnecki, Adal Sabri, Matthias Weiss, Diego Krapf
    Academic press:
    New Journal of Physics (rok: 2021, tom: 23, strony: 53018), Wydawca: IOP
    Status:
    Published
    DOI:
    10.1088/1367-2630/abf204 - link to the publication
  13. Classification of random trajectories based on the fractional Lévy stable motion
    Authors:
    Joanna Janczura, Krzysztof Burnecki, Monika Muszkieta, Aleksander Stanislavsky, Aleksander Weron
    Academic press:
    Chaos, Solitons and Fractals (rok: 2022, tom: 154, strony: 111606), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.chaos.2021.111606 - link to the publication
  14. Time-changed fractional Black-Scholes interest rate model for pricing equity warrants
    Authors:
    Foad Shokrollahi, Marcin Magdziarz
    Academic press:
    IEEE Access (rok: 2023, ), Wydawca: Institute of Electrical and Electronics Engineers
    Status:
    Submitted
  15. Lévy walks with rests: Long-time analysis
    Authors:
    Marcin Magdziarz, Władysław Szczotka
    Academic press:
    PHYSICAL REVIEW E (rok: 2022, tom: 105, strony: 14114), Wydawca: APS
    Status:
    Published
    DOI:
    10.1103/PhysRevE.105.014114 - link to the publication
  16. A computational weighted finite difference method for American and barrier options in subdiffusive Black–Scholes model
    Authors:
    Grzegorz Krzyżanowski, Marcin Magdziarz
    Academic press:
    Commun Nonlinear Sci Numer Simulat (rok: 2021, tom: 96, strony: 105676), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2020.105676 - link to the publication
  17. Stochastic representation of processes with resetting
    Authors:
    Marcin Magdziarz, Kacper Taźbierski
    Academic press:
    Physical Review E (rok: 2022, tom: 106, strony: 14147), Wydawca: APS
    Status:
    Published
    DOI:
    10.1103/PhysRevE.106.014147 - link to the publication
  18. Identifying heterogeneous diffusion states in the cytoplasm by a hidden Markov model
    Authors:
    Joanna Janczura, Michał Balcerek, Krzysztof Burnecki, Adal Sabri, Matthias Weiss, Diego Krapf
    Academic press:
    New Journal of Physics (rok: 2021, tom: 23, strony: 53018), Wydawca: IOP
    Status:
    Published
    DOI:
    10.1088/1367-2630/abf204 - link to the publication
  19. Zero Black-Derman-Toy Model in Catastrophic Events: COVID-19 Performance Analysis
    Authors:
    Grzegorz Krzyżanowski, Andrés Sosa
    Academic press:
    The Journal of Derivatives (rok: 2022, tom: 30 (1), strony: 103-118), Wydawca: PMR
    Status:
    Published
    DOI:
    10.3905/jod.2022.1.164 - link to the publication
  20. Stochastic representation of processes with resetting
    Authors:
    Marcin Magdziarz, Kacper Taźbierski
    Academic press:
    Physical Review E (rok: 2022, tom: 106, strony: 14147), Wydawca: APS
    Status:
    Published
    DOI:
    10.1103/PhysRevE.106.014147 - link to the publication
  21. Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermitemethod
    Authors:
    Łukasz Płociniczak, Mateusz Świtała
    Academic press:
    Fractional Calculus and Applied Analysis (rok: 2022, tom: 25, strony: 1651–1687), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s13540-022-00063-x - link to the publication
  22. Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermitemethod
    Authors:
    Łukasz Płociniczak, Mateusz Świtała
    Academic press:
    Fractional Calculus and Applied Analysis (rok: 2022, tom: 25, strony: 1651–1687), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s13540-022-00063-x - link to the publication
  23. Lévy walks with rests: Long-time analysis
    Authors:
    Marcin Magdziarz, Władysław Szczotka
    Academic press:
    PHYSICAL REVIEW E (rok: 2022, tom: 105, strony: 14114), Wydawca: APS
    Status:
    Published
    DOI:
    10.1103/PhysRevE.105.014114 - link to the publication
  24. Simulation and tracking of fractional particles motion. From microscopy video to statistical analysis. A Brownian bridge approach
    Authors:
    Monika Muszkieta, Joanna Janczura , Aleksander Weron
    Academic press:
    Applied Mathematics and Computation (rok: 2021, tom: 396, strony: 125902), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.amc.2020.125902 - link to the publication
  25. A computational weighted finite difference method for American and barrier options in subdiffusive Black–Scholes model
    Authors:
    Grzegorz Krzyżanowski, Marcin Magdziarz
    Academic press:
    Commun Nonlinear Sci Numer Simulat (rok: 2021, tom: 96, strony: 105676), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2020.105676 - link to the publication
  26. Zero Black-Derman-Toy Interest Rate Model
    Authors:
    Grzegorz Krzyżanowski, Ernesto Mordecki, Andrés Sosa
    Academic press:
    The Journal of Fixed Income (rok: 2022, tom: 31(3), strony: 93-111), Wydawca: PMR
    Status:
    Published
    DOI:
    10.3905/jfi.2021.1.122 - link to the publication
  27. About subordinated generalizations of 3 classical models of option pricing
    Authors:
    Michał Balcerek, Grzegorz Krzyżanowski, Marcin Magdziarz
    Academic press:
    Mathematica Applicanda (rok: 2023, ), Wydawca: PTM
    Status:
    Submitted
  28. Classification of particle trajectories in living cells: Machine learning versus statistical testing hypothesis for fractional anomalous diffusion
    Authors:
    Joanna Janczura, Patrycja Kowalek, Hanna Loch-Olszewska, Janusz Szwabiński, Aleksander Weron
    Academic press:
    PHYSICAL REVIEW E (rok: 2020, tom: 102, strony: 32402), Wydawca: APS
    Status:
    Published
    DOI:
    10.1103/PhysRevE.102.032402 - link to the publication
  29. Simulation and tracking of fractional particles motion. From microscopy video to statistical analysis. A Brownian bridge approach
    Authors:
    Monika Muszkieta, Joanna Janczura , Aleksander Weron
    Academic press:
    Applied Mathematics and Computation (rok: 2021, tom: 396, strony: 125902), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.amc.2020.125902 - link to the publication
  30. Zero Black-Derman-Toy Model in Catastrophic Events: COVID-19 Performance Analysis
    Authors:
    Grzegorz Krzyżanowski, Andrés Sosa
    Academic press:
    The Journal of Derivatives (rok: 2022, tom: 30 (1), strony: 103-118), Wydawca: PMR
    Status:
    Published
    DOI:
    10.3905/jod.2022.1.164 - link to the publication
  31. A computational weighted finite difference method for American and barrier options in subdiffusive Black–Scholes model
    Authors:
    Grzegorz Krzyżanowski, Marcin Magdziarz
    Academic press:
    Commun Nonlinear Sci Numer Simulat (rok: 2021, tom: 96, strony: 105676), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2020.105676 - link to the publication
  32. Classification of particle trajectories in living cells: Machine learning versus statistical testing hypothesis for fractional anomalous diffusion
    Authors:
    Joanna Janczura, Patrycja Kowalek, Hanna Loch-Olszewska, Janusz Szwabiński, Aleksander Weron
    Academic press:
    PHYSICAL REVIEW E (rok: 2020, tom: 102, strony: 32402), Wydawca: APS
    Status:
    Published
    DOI:
    10.1103/PhysRevE.102.032402 - link to the publication
  33. Lévy walks with rests: Long-time analysis
    Authors:
    Marcin Magdziarz, Władysław Szczotka
    Academic press:
    PHYSICAL REVIEW E (rok: 2022, tom: 105, strony: 14114), Wydawca: APS
    Status:
    Published
    DOI:
    10.1103/PhysRevE.105.014114 - link to the publication
  34. Zero Black-Derman-Toy Interest Rate Model
    Authors:
    Grzegorz Krzyżanowski, Ernesto Mordecki, Andrés Sosa
    Academic press:
    The Journal of Fixed Income (rok: 2022, tom: 31(3), strony: 93-111), Wydawca: PMR
    Status:
    Published
    DOI:
    10.3905/jfi.2021.1.122 - link to the publication

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