Przejdź do treści

Uniwersytet Śląski w Katowicach

asa
asa
Instytut Matematyki

prof. dr hab. Katarzyna Horbacz

Katarzyna Horbacz
Stanowisko:

Grupa:

Specjalność:

Pokój:

Telefon:

e-mail:

Logo ORCID

Profesor

Pracownicy badawczo-dydaktyczni

Teoria Prawdopodobieństwa

565

(32) 359 16 24

katarzyna.horbacz@us.edu.pl

0000-0003-2900-0031

Pełnione funkcje Pełnione funkcje

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

01.10.2016

17.04.2019

Plan zajęć Plan zajęć

W semestrze letnim roku 2019/2020 zajęcia odbywają się w sposób zdalny.

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.

Materiały konferencyjne / rozdziały w monografiach

  1. T. Bielaczyc i K. Horbacz, Dimensions of invariant measures for continuous random dynamical systems, red. T. Simos oraz C. Tsitouras, AIP Publishing (vol. 1648 of AIP Conference Proceedings), Melville, New York, 2015, pp. 850025-1 – 850025-4, ISBN: 978-0-7354-1854-7, doi: 10.1063/1.4913080
  2. D. Czapla i K. Horbacz, The stability of Markov chains with partially equicontinuous transition structure, red. T. Simos oraz C. Tsitouras, AIP Publishing (vol. 1738 of AIP Conference Proceedings), Melville, New York, 2016, pp. 480039-1 – 480039-4, ISBN: 978-0-7354-1854-7, doi: 10.1063/1.4952275.
  3. K. Horbacz, The central limit theorem for continuous random dynamical systems, red. T. Simos oraz C. Tsitouras, AIP Publishing (vol. 1863 of AIP Conference Proceedings),  Melville, New York, 2017, pp. 560026-1 – 560026-4, ISBN: 978-0-7354-1854-7, 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, red. T. Simos oraz C. Tsitouras, AIP Publishing (vol. 1978 of AIP Conference Proceedings), Melville, New York, 2018, pp. 470008-1 – 470008-4, ISBN: 978-0-7354-1854-7, doi: 10.1063/1.5044078.
  5. D. Czapla, K. Horbacz i H. Wojewódka, Limit theorems for certain stochastic models for gene regulatory networks, red. T. Simos oraz C. Tsitouras, AIP Publishing (vol. 1978 of AIP Conference Proceedings), Melville, New York, 2018, pp. 470051-1 – 470051-4, ISBN: 978-0-7354-1854-7, doi: 10.1063/1.5044121
  6. D. Czapla, K. Horbacz i H. Wojewódka Limit theorems for a Markov Model of Autoregulated Gene Expression, 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.

Prace przyjęte do druku

  1. D. Czapla, K. Horbacz i H. Wojewódka-Ściążko, The Strassen Invariance Principle for Certain Non-stationary Markov-Feller Chains, przyjęta w Asymptotic Analysis (2020), doi: 10.3233/ASY-191592, arXiv: 1810.07300.
  2. 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, opublikowana online w Stochastic Analysis and Applicationsdoi: 10.1080/07362994.2020.1798252 (2020), arXiv: 1909.06777.
  3. D. Czapla, K. Horbacz i H. Wojewódka-Ściążko, A Useful Version of the Central Limit Theorem for a General Class of Markov Chains, przyjęta w J.Math. Anal. Appl. 484(1) (2020), 123725, doi: 10.1016/j.jmaa.2019.123725, arXiv: 1804.09220.
  4. D. Czapla, S. C. Hille, K.Horbacz, H. Wojewódka- Ściążko, On the Continuous Dependence of the Stationary Distribution of a Piecewise Deterministic Markov Process on its Jump Intensity, przyjęta w AIP Publishing (AIP Conference Proceedings).
  5. D. Czapla, K.Horbacz, H. Wojewódka- Ściążko, On the Connection between Exponential Ergodicity of a Piecewise Deterministic Markov Process and the Chain Given by its Post-jump Locations, przyjęta w AIP Publishing (AIP Conference Proceedings).
  6. D. Czapla, K. Horbacz, H. Wojewódka-Ściążko, A note on absolute continuity of stationary distributions of some piecewise-deterministic Markov process, przyjęta w AIP Publishing (AIP Conference Proceedings).

Prace w trakcie recenzji

  1. D. Czapla, K.Horbacz, H. Wojewódka- Ściążko, On absolute continuity of invariant measures associated with a piecewise deterministic Markov processes with random switching between flows, wysłana do Nonlinear Analysis: Theory, Methods & Applications, arXiv: 2004.06798.

Prace przygotowywane

  1. D. Czapla, K.Horbacz, H. Wojewódka- Ściążko, Exponential ergodicity for a class of piecewise-deterministic Markov processes with random switching between flows.
return to top