Department of Probability Theory
Institute of Mathematics
University of Silesia



PL

Katarzyna Horbacz – List of publications

Journal articles:

  1. Dynamical systems with multiplicative perturbations, Ann. Polon. Math. 50 (1989), 11--26.
  2. Asymptotic stability of dynamical systems with multiplicative perturbations, Ann. Polon. Math. 50 (1989), 209--218.
  3. Statistical properties of the Ejgielies model of a cogged bit, Applicationes Mathematicae 21.1 (1991), 15--26.
  4. Invariant densities for one-dimensional random dynamical systems, Univ. Iagell. Acta Math. 28 (1991), 101--106.
  5. Weak and strong asymptotic stability, Bull. Polish Acad. Sci. Math. 40.1 (1992), 271--282.
  6. Dynamical systems with multiplicative perturbations: The strong convergence of measures, Ann. Polon. Math. 58 (1993), 85--93.
  7. Randomly connected dynamical systems -- asymptotic stability, Ann. Polon. Math. 68.1 (1998), 31--50.
  8. Randomly connected dynamical systems on Banach spaces, Stoch. Anal. Appl. 19.4 (2001), 519--543.
  9. with T. Szarek, Continuous iterated function systems on Polish spaces, Bull. Polish Acad. Sci. Math. 49.2 (2001), 191--202.
  10. Asymptotic stability of a system of randomly connected transformations on Polish spaces, Ann. Polon. Math. 76.3 (2001), 197--211.
  11. Randomly connected differential equations with Poisson type perturbations, Nonlinear Studies 9.1 (2002), 81--98.
  12. Invariant measures related with randomly connected Poisson driven differential equations, Ann. Polon. Math. 79.1 (2002), 31--44 .
  13. Random dynamical systems with jumps, J. Appl. Probab. 41 (2004), 890--910.
  14. with J. Myjak and T. Szarek, On stability of some general random dynamical system, J. Statist. Phys. 119 (2005), 35--60.
  15. with J. Myjak and T. Szarek, Stability of random dynamical systems on Banach spaces, Positivity 10.3 (2006), 517--538.
  16. Asymptotic stability of a semigroup generated by randomly connected Poisson driven differential equations, Boll. Uni. Mat. Ital. (8) 9-B (2006), 545--566.
  17. Pointwise and Rényi dimensions of an invariant measures of random dynamical systems with jumps, J. Statist. Phys. 122.5 (2006), 1041--1059.
  18. with T. Szarek, Irreducible Markov systems on Polish spaces, Studia Math. 177.3 (2006), 285--295.
  19. Invariant measures for random dynamical systems, Dissertationes Math. 451 (2008).
  20. with T. Bielaczyc, The Hausdorff dimension of invariant measures for random dynamical systems, J. Math. Anal. Appl. 391 (2012), 298--311.
  21. Continuous random dynamical systems, J. Math. Anal. Appl. 408 (2013), 623--637.
  22. Stability of the heat equation driven by an impulsive noise, Chaos, Solitons and Fractals, 57 (2013), 1--8.
  23. with D. Czapla, Equicontinuity and Stability Properties of Markov Chains Arising from Iterated Function Systems on Polish Spaces, Stoch. Anal. Appl. 32.1 (2014), 1--29.
  24. with T. Bielaczyc, Dimensions of invariant measures for continuous random dynamical systems, AIP Conference Proceedings 1648, 850025 (2015).
  25. with M. Ślęczka, Law of Large Numbers for Random Dynamical Systems, J. Statist. Phys. 162 (2016), 671--684 (DOI 10.1007/s10955-015-1423-6).
  26. with S. Hille, T. Szarek and H. Wojewódka, Law of the iterated logarithm for some Markov operators, Asymptotic Analysis 97 (2016), 91--112 (DOI: 10.3233/ASY-151344).
  27. with T. Bielaczyc, Dimensions of invariant measures for continuous random dynamical systems, Math. Meth. Appl. Sci. 39 (2016), 3947--3960 (DOI: 10.1002/mma.3836).
  28. with D. Czapla, The stability of Markov chains with partially equicontinuous transition structure, AIP Conference Proceedings 1738, 480039 (2016) (DOI: 10.1063/1.4952275).
  29. with S. Hille, T. Szarek, H. Wojewódka, Limit theorems for some Markov operators, J. Math. Anal. Appl. 443 (2016), 385--408.
  30. Strong law of large numbers for continuous random dynamical systems, Statistics and Probability Letters 118 (2016), 70--79.
  31. The Central Limit Theorem for Random Dynamical Systems, Journal of Statistical Physics 164 (2016), 1261-1291 (DOI: 10.1007/s10955-016-1601-1) .
  32. with S. Hille, 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, accepted for publication by Annales Mathématiques Blaise Pascal.
  33. The Central Limit Theorem for Continuous Random Dynamical Systems, AIP Conference Proceedings 1863, 560026 (2017) (DOI: 10.1063/1.4992709) .

Katowice, August 2017
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