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

Grant no: 2019/34/E/ST1/00360

Funding agency: National Science Centre (NCN), Poland

Funding scheme: Sonata Bis

Funding period: 2020-03-30 -- 2023-09-29 (42 months)

Budget: 576 900 PLN

Title in Polish: Analiza probabilistyczna, numeryczna i statystyczna procesów sub- i superdyfuzji

Research team

Principal Investigator (Kierownik Grantu)

· Marcin Magdziarz (WUST, Wrocław, PL)

Investigators (Wykonawcy)

· Joanna Janczura

· Grzegorz Krzyżanowski

· Mateusz Świtała

· Kacper Taźbierski

· Aleksandra Rogalska

Tasks

1. Asymptotic properties of dependent continuous time random walks

2. Numerical methods for subdiffusive fractional differential equations of the Black-Scholes type

3. Parameter estimation for subdiffusive fractional differential equations

Publications

1. S. Carnaffan, M. Magdziarz, W. Szczotka „Nonlinear dynamics of continuous-time random walks in inhomogeneous medium” Chaos 30, 063135 (2020)

2. J. Janczura et al. „Classification of particle trajectories in living cells: Machine learning versus statistical testing hypothesis for fractional anomalous diffusion” Phys. Rev. E 102, 032402 (2020)

3. M. Muszkieta, J. Janczura, A. Weron „Simulation and tracking of fractional particles motion. From microscopy video to statistical analysis. A Brownian bridge approach”, Applied Mathematics and Computation 396, 125902 (2021)

4. G. Krzyżanowski, M. Magdziarz „A computational weighted finite difference method for American and barrier options in subdiffusive Black–Scholes model”, Commun Nonlinear Sci Numer Simulat 96, 105676 (2021)

5. J. Janczura et al. „Identifying heterogeneous diffusion states in the cytoplasm by a hidden Markov model”, New J. Phys. 23, 053018 (2021)

6. G. Krzyżanowski, E. Mordecki, A. Sosa „Zero Black-Derman-Toy Interest Rate Model”, The Journal of Fixed Income 2021.1.122 (2021)

7. M. Magdziarz, W. Szczotka „Lévy walks with rests: Long-time analysis”, Phys. Rev. E 105, 014114 (2022)

8. J. Janczura et al. „Classification of random trajectories based on the fractional Lévy stable motion”, Chaos, Solitons and Fractals 154, 111606 (2022)

9. Ł. Płociniczak, M. Switała „Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method”, Fractional Calculus and Applied Analysis 25:1651–1687 (2022)

10. M. Magdziarz, K. Tazbierski, „Stochastic representation of processes with resetting”, Phys. Rev. E 106, 014147 (2022)

11. G. Krzyżanowski, A. Sosa, „Zero Black-Derman-Toy Model in CatastrophicEvents: COVID-19 Performance Analysis”, The Journal of Derivatives 30(1), 103-118 (2022)

12. M. Muszkieta, J, Janczura „A compressed sensing approach to interpolation of fractional Brownian trajectories for a single particle tracking experiment”, Applied Mathematics and Computation 446, 127900 (2023)

13. M. Balcerek, G. Krzyżanowski, M. Magdziarz „About subordinated generalizations of 3 classical models of option pricing”, submitted (2022)

14. G. Krzyżanowski, M. Magdziarz „A tempered subdiffusive Black-Scholes model”, submitted (2022)

15. F. Shokrollahi, M. Magdziarz „Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate”, submitted (2022)

Conferences and Seminars

1. 21st ECMI Conference on Industrial and Applied Mathematics, Wuppertal (online), 13-15.04.2021, title of the talk: "Fractional processes with switching. Application to cell dynamics and solar flares modeling")

2. Seminar on Stochastic and Numerical Methods, WUST, 8.12.2021, title of the talk „Classification of random trajectories using Fractional Brownian motion” .

3. Seminar on Stochastic and Numerical Methods, WUST, 24.03.2021, title of the talk „Simulation and recognition of particle fractional dynamics. From microscopy records to stochastic analysis. Application of Brownian bridge.”

4. Workshop “Fractional Differential Equations”, The Isaac Newton Institute, Cambridge, England, 2022 r. Invited talk „Stochastic representation of processes with resetting”.

5. Probability and Analysis 2022, Contributed Paper Session “Diffusive limits of isotropic continuous Levy walks”

6. Seminarium z Metod Stochastyczych i Numerycznych, PWr, 08.12.2021, " Klasyfikacja trajektorii losowych z użyciem ułamkowego ruchu stabilnego"

7. Seminarium z Metod Stochastyczych i Numerycznych, PWr, 24.03.2021, " Symulowanie i rozpoznawanie dynamiki ułamkowej cząstek. Od nagrań mikroskopijnych do analizy statystycznej. Podejście z wykorzystaniem mostu Browna"

8. Seminar on Applied Mathematics, IM PAN, Sopot, Poland. Talk: ''Numerical analysis of the Erdelyi-Kober fractional diffusion equation'', 23 September 2022

9. Conference: ''Mathematics for Society: Health, Industry and Sustainable Development'', Gdańsk University of Technology, Gdańsk, Poland. Talk: Capillary rise problem and numerical methods for fractional diffusion equation'', 24 November 2022