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Instytut Matematyki
Logo Europejskie Miasto Nauki Katowice 2024
home link Pracownicy prof. dr hab. Katarzyna Horbacz

prof. dr hab. Katarzyna Horbacz

Katarzyna Horbacz
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 Profesor

Pracownicy badawczo-dydaktyczni

Teoria Prawdopodobieństwa

565

(32) 359 16 24

katarzyna.horbacz@us.edu.pl

0000-0003-2900-0031
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Dyrektor Instytutu Matematyki

Członek Rady Naukowej Instytutu Matematyki

CV CV
Magister

Doktor

Doktor habilitowany

Profesor nauk matematycznych

 1984, Uniwersytet Śląski, Katowice

1991, Uniwersytet Śląski, Katowice

20.01.2009

17.04.2019
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Mój plan zajęć dostępny jest na tej stronie.

Publikacje Publikacje

Artykuły naukowe

  1. K. Horbacz, Dynamical systems with multiplicative perturbations, Ann. Polon. Math. 50 (1989), 11–26.
  2. K. Horbacz, Asymptotic stability of dynamical systems with multiplicative perturbations, Ann. Polon. Math. 50 (1989), 209–218.
  3. K. Horbacz, Statistical properties of the Ejgielies model of a cogged bit, Applicationes Mathematicae 21.1 (1991), 15–26.
  4. K. Horbacz, Invariant densities for one-dimensional random dynamical systems, Univ. Iagell. Acta Math. 28 (1991), 101–106.
  5. K. Horbacz, Weak and strong asymptotic stability, Bull. Polish Acad. Sci. Math. 40.1 (1992), 271–282.
  6. K. Horbacz, Dynamical systems with multiplicative perturbations: The strong convergence of measures, Ann. Polon. Math. 58 (1993), 85–93.
  7. K. Horbacz, Randomly connected dynamical systems – asymptotic stability, Ann. Polon. Math. 68.1 (1998), 31–50.
  8. K. Horbacz i T. Szarek, Randomly connected dynamical systems on Banach spaces, Stoch. Anal. Appl. 19.4 (2001), 519–543.
  9. K. Horbacz i T. Szarek, Continuous iterated function systems on Polish spaces, Bull. Polish Acad. Sci. Math. 49.2 (2001), 191–202.
  10. K. Horbacz, Asymptotic stability of a system of randomly connected transformations on Polish spaces, Ann. Polon. Math. 76.3 (2001), 197–211.
  11. K. Horbacz, Randomly connected differential equations with Poisson type perturbations, Nonlinear Studies 9.1 (2002), 81–98.
  12. K. Horbacz, Invariant measures related with randomly connected Poisson driven differential equations, Ann. Polon. Math. 79.1 (2002), 31–44.
  13. K. Horbacz, Random dynamical systems with jumps, J. Appl. Probab. 41 (2004), 890–910.
  14. K. Horbacz, J. Myjak i T. Szarek, On stability of some general random dynamical system, J. Statist. Phys. 119 (2005), 35–60.
  15. K. Horbacz, J. Myjak i T. Szarek, Stability of random dynamical systems on Banach spaces, Positivity 10.3 (2006), 517–538.
  16. K. Horbacz, Asymptotic stability of a semigroup generated by randomly connected Poisson driven differential equations, Boll. Uni. Mat. Ital. (8) 9-B (2006), 545–566.
  17. K. Horbacz, Pointwise and R ́enyi dimensions of an invariant measures of random dynamical systems with jumps, J. Statist. Phys. 122.5 (2006), 1041–1059.
  18. K. Horbacz i T. Szarek, Irreducible Markov systems on Polish spaces, Studia Math. 177.3 (2006), 285–295.
  19. K. Horbacz, Invariant measures for random dynamical systems, Dissertationes Math. 451 (2008).
  20. T. Bielaczyc i K. Horbacz, The Hausdorff dimension of invariant measures for random dynamical systems, J. Math. Anal. Appl. 391 (2012), 298–311.
  21. K. Horbacz, Continuous random dynamical systems, J. Math. Anal. Appl. 408 (2013), 623–637.
  22. K. Horbacz, Stability of the heat equation driven by an impulsive noise, Chaos, Solitons and Fractals 57 (2013), 1–8.
  23. D. Czapla i K. Horbacz, Equicontinuity and stability properties of Markov chains arising from Iterated Function Systems on Polish Spaces, Stoch. Anal. Appl. 32.1 (2014), 1–29, doi: 10.1080/07362994.2013.836716.
  24. K. Horbacz i M. Śleczka, Law of large numbers for random dynamical systems, J. Statist. Phys. 162 (2016), 671–684.
  25. S. Hille, K. Horbacz i T. Szarek, Existence of a unique invariant measure for a class of equicontinuous Markov operators with application to a stochastic model for an autoregulated gene, Annales Mathematiques Blaise Pascal 23 (2016), 171–217.
  26. S. Hille, K. Horbacz, T. Szarek i H. Wojewódka, Limit theorems for some Markov operators, J. Math. Anal. Appl. 443 (2016), 385–408.
  27. S. Hille, K. Horbacz, T. Szarek i H. Wojewódka, Law of the iterated logarithm for some Markov operators, Asymptotic Analysis 97 (2016), 91–112.
  28. K. Horbacz, Strong law of large numbers for continuous random dynamical systems, Statistics and Probability Letters 118 (2016), 70–79.
  29. K. Horbacz, The central limit theorem for random dynamical systems, J. Statist. Phys. 164 (2016), 1261–1291.
  30. T. Bielaczyc i K. Horbacz, Dimension of invariant measures for continuous random dynamical systems, Math. Meth. Appl. Sci. 39 (2016), 3947–3960.
  31. D. Czapla, S. Hille, K.Horbacz, H. Wojewódka-Ściążko Continuous dependence of an invariant measure on the jump rate of a piecewise-deterministic Markov process, Mathematical Biosciences and Engineering, 17(20) (2020), 1059-1073, doi: 10.3934/mbe.2020056, arXiv: 1909.05396.
  32. D. Czapla, K. Horbacz i H. Wojewódka-Ściążko, Ergodic properties of some piecewise deterministic Markov process with application to a gene expression model, Stochastic Processes and their Applications 130 (2020), 2851–2885, doi:10.1016/j.spa.2019.08.006, arXiv: 1804.09220.
  33. D. Czapla, K. Horbacz i H. Wojewódka-Ściążko, A Useful Version of the Central Limit Theorem for a General Class of Markov Chains, J.Math. Anal. Appl. 484(1) (2020), art. no. 123725, doi: 10.1016/j.jmaa.2019.123725, arXiv: 1804.09220.
  34. D. Czapla, K. Horbacz i H. Wojewódka-Ściążko, The Strassen Invariance Principle for Certain Non-stationary Markov-Feller Chains, Asymptotic Analysis 121(1) (2021), 1-34, doi: 10.3233/ASY-191592, arXiv: 1810.07300.
  35. D. Czapla, S. C Hille, K. Horbacz, H. Wojewódka- Ściążko, The Law of the Iterated Logarithm for a Piecewise Deterministic Markov Process Assured by the Properties of the Markov Chain Given by Its Post-jump Locations, Stochastic Analysis and Applications 39(2) (2021), 357-379, doi: 10.1080/07362994.2020.1798252, arXiv: 1909.06777.
  36. D. Czapla, K.Horbacz, H. Wojewódka- Ściążko, On absolute continuity of invariant measures associated with a piecewise deterministic Markov process with random switching between flows, Nonlinear Analysis 213 (2021), art. no. 112522, doi: 10.1016/j.na.2021.112522, arXiv: 2004.06798.
  37. D. Czapla, K.Horbacz, H. Wojewódka-Ściążko, Exponential ergodicity in the bounded-Lipschitz distance for some piecewise-deterministic Markov processes with random switching between flows, Nonlinear Analysis 215 (2022), art. no. 112678, doi: 10.1016/j.na.2021.112678, arXiv: 2011.07671.
  38. D. Czapla, K.Horbacz, H. Wojewódka-Ściążko, The Central Limit Theorem for Markov Processes that are Exponentially Ergodic in the Bounded-Lipschitz Norm, Qualitative Theory of Dynamical Systems 23(1) (2024), art. no. 7, doi.org/10.1007/s12346-023-00862-4, arXiv: 2210.11963. 

Materiały konferencyjne / rozdziały w monografiach

  1. T. Bielaczyc i K. Horbacz, Dimensions of invariant measures for continuous random dynamical systems, in: Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM 2014), red. T. Simos oraz C. Tsitouras, AIP Publishing (vol. 1648 of AIP Conference Proceedings), Melville, New York, 2015, pp. 850025-1 – 850025-4, ISBN: 978-0-7354-1287-3, doi: 10.1063/1.4913080
  2. D. Czapla i K. Horbacz, The stability of Markov chains with partially equicontinuous transition structure, in: International Conference on Numerical Analysis and Applied Mathematics 2015 (ICNAAM 2015), red. T. Simos oraz C. Tsitouras, AIP Publishing (vol. 1738 of AIP Conference Proceedings), Melville, New York, 2016, pp. 480039-1 – 480039-4, ISBN: 978-0-7354-1392-4, doi: 10.1063/1.4952275.
  3. K. Horbacz, The central limit theorem for continuous random dynamical systems, in: International Conference on Numerical Analysis and Applied Mathematics 2016 (ICNAAM 2016), red. T. Simos oraz C. Tsitouras, AIP Publishing (vol. 1863 of AIP Conference Proceedings),  Melville, New York, 2017, pp. 560026-1 – 560026-4, ISBN: 978-0-7354-1538-6, doi: 10.1063/1.4992709.
  4. D. Czapla, K. Horbacz i H. Wojewódka, The strong law of large numbers for certain piecewise-deterministic Markov processes with application to a gene expression model, in: International Conference on Numerical Analysis and Applied Mathematics 2017 (ICNAAM 2017), red. T. Simos oraz C. Tsitouras, AIP Publishing (vol. 1978 of AIP Conference Proceedings), Melville, New York, 2018, pp. 470008-1 – 470008-4, ISBN: 978-0-7354-1690-1, doi: 10.1063/1.5044078.
  5. D. Czapla, K. Horbacz i H. Wojewódka, Limit theorems for certain stochastic models for gene regulatory networks, in: International Conference on Numerical Analysis and Applied Mathematics 2017 (ICNAAM 2017), red. T. Simos oraz C. Tsitouras, AIP Publishing (vol. 1978 of AIP Conference Proceedings), Melville, New York, 2018, pp. 470051-1 – 470051-4, ISBN: 978-0-7354-1690-1, doi: 10.1063/1.5044121
  6. D. Czapla, K. Horbacz i H. Wojewódka-Ściążko, Limit theorems for a Markov Model of Autoregulated Gene Expression, in: International Conference on Numerical Analysis and Applied Mathematics 2018 (ICNAAM 2018), red. T. Simos oraz C. Tsitouras, AIP Publishing (vol. 2216 of AIP Conference Proceedings), Melville, New York, 2019, pp. 450055 -1 – 450055 -4, ISBN: 978-0-7354-1854-7, doi: 10.1063/1.5114522.
  7. D. Czapla, K. Horbacz i H. Wojewódka-Ściążko, On the Connection between Exponential Ergodicity of a Piecewise Deterministic Markov Process and the Chain Given by its Post-jump locations, in: International Conference on Numerical Analysis and Applied Mathematics 2019 (ICNAAM 2019), red. T. Simos oraz C. Tsitouras, AIP Publishing (vol. 2293 of AIP Conference Proceedings), Melville, New York, 2020, 420056-1 – 420056-4, ISBN: 978-0-7354-4025-8, doi: 10.1063/5.0026519.
  8. D. Czapla, S.C. Hille, K. Horbacz i H. Wojewódka-Ściążko, On the continuous dependence of the stationary distribution of a piecewise deterministic Markov process on its jump intensity, in: International Conference on Numerical Analysis and Applied Mathematics 2019 (ICNAAM 2019), red. T. Simos oraz C. Tsitouras, AIP Publishing (vol. 2293 of AIP Conference Proceedings), Melville, New York, 2020, 420083-1 – 420083-4, ISBN: 978-0-7354-4025-8, doi: 10.1063/5.0027213.
  9. D. Czapla, S.C. Hille, K. Horbacz i H. Wojewódka-Ściążko, A note on absolute continuity of stationary distributions of some piecewise-deterministic Markov process, in: International Conference on Numerical Analysis and Applied Mathematics 2020 (ICNAAM 2020), red. T. Simos oraz C. Tsitouras, AIP Publishing (vol. 2425 of AIP Conference Proceedings), Melville, New York, 2022, 420015-1 – 420015-4, ISBN: 978-0-7354-4182-8, doi: 10.1063/5.0081329.
  10. D. Czapla, S.C. Hille, K. Horbacz i H. Wojewódka-Ściążko, A criterion on exponential ergodicity in the bounded-Lipschitz distance for some piecewise-deterministic Markov processes with random switching, in: International Conference on Numerical Analysis and Applied Mathematics 2021 (ICNAAM 2021), red. T. Simos oraz C. Tsitouras, AIP Publishing (vol. 2849 of AIP Conference Proceedings), Melville, New York, 2023, 450015-1 – 450015-4, ISBN: 978-0-7354-4589-5, doi: 10.1063/5.0163391.
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