Artykuły naukowe
A criterion of asymptotic stability for Markov - Feller E-chains on Polish spaces, Ann. Polon. Math. 105 (2012), no. 3, 267-291. MR2950661, doi: 10.4064/ap105-3-5.
Equicontinuity and stability properties of Markov Chains arising from Iterated Function Systems with place dependent probabilities (with K. Horbacz), Stoch. Anal. Appl. 32 (2014), no. 1, 1-29. MR3175812, doi: 10.1080/07362994.2013.836716.
A criterion on asymptotic stability for partially equicontinuous Markov operators, Stochastic Processes and their Applications 128 (2018), no. 11, 3656-3678, doi: 10.1016/j.spa.2017.12.006
Ergodic properties of some piecewise-deterministic Markov process with application to gene expression modelling (with K. Horbacz and H. Wojewódka - Ściążko), Stochastic Processes and their Applications 130 (2020), no. 5, 2851-2885, doi: 10.1016/j.spa.2019.08.006, arXiv: 1707.06489.
Exponential ergodicity of some Markov dynamical systems with application to a Poisson driven stochastic differential equation (with J. Kubieniec), Dynamical Systems - An International Journal 34 (2019), no. 1, 130-156 doi: 10.1080/14689367.2018.1485879, arXiv: 1801.06684.
A useful version of the central limit theorem for a general class of Markov Chains (with K. Horbacz and H. Wojewódka - Ściążko), J. Math. Anal. Appl. 484 (2020), no. 1, 123725, doi: 10.1016/j.jmaa.2019.123725, arXiv: 1804.09220.
Continuous dependence of an invariant measure on the jump rate of a piecewise-deterministic Markov chain (with S. C. Hille, K. Horbacz and H. Wojewódka-Ściążko), Mathematical Biosciences and Engineering 17 (2020), no. 2, 1059-1073, doi: 10.3934/mbe.2020056, arXiv: 1909.05396.
The Strassen Invariance Principle for Certain Non-Stationary Markov-Feller Chains (with K. Horbacz and H. Wojewódka - Ściążko), Asymptotic Analysis 121 (2021), no. 1, 1-34, doi: 10.3233/ASY-191592, arXiv: 1810.07300.
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 (with S. C. Hille, K. Horbacz and H. Wojewódka - Ściążko), Stoch. Anal. Appl. 39 (2021), no. 2, 357-379, doi: 10.1080/07362994.2020.1798252, arXiv: 1909.06777.
On absolute continuity of invariant measures associated with a piecewise-deterministic Markov process with random switching between flows (with K. Horbacz and H. Wojewódka - Ściążko), Nonlinear Analysis 213 (2021), 112522, doi: 10.1016/j.na.2021.112522, arXiv: 2004.06798.
Exponential ergodicity in the bounded-Lipschitz distance for some piecewise-deterministic Markov processes with random switching between flows (with K. Horbacz and H. Wojewódka - Ściążko), Nonlinear Analysis 215 (2022), 112678, doi: 10.1016/j.na.2021.112678, arXiv: 2011.07671.
The central limit theorem for Markov processes that are exponentially ergodic in the bounded-Lipschitz norm (with K. Horbacz and H. Wojewódka - Ściążko), Qualitative Theory of Dynamical Systems 23 (2024), no. 1, 7, doi: 10.1007/s12346-023-00862-4, arXiv: 2210.11963.
On the Existence and Uniqueness of Stationary Distributions for Some Piecewise Deterministic Markov Processes with State-Dependent Jump Intensity, Results in Mathematics 79 (2024), 177, doi: 10.1007/s00025-024-02195-3, arXiv: 2303.11576.
On the existence of geometrically attracting measures for random iterated function systems with varying transformations sets (with R. Kapica and M. Ślęczka)
Recenzowane materiały konferencyjne
The stability of Markov chains with partially equicontinuous transition structure (with K. Horbacz), AIP Conference Proceedings 1738 (2016), 480039, doi: 10.1063/1.4952275
The Strong Law of Large Numbers for Certain Piecewise-Deterministic Markov Processes with Application to a Gene Expression Model (with K. Horbacz and H. Wojewódka), AIP Conference Proceedings 1978 (2018), 470008, doi: 10.1063/1.5044078
Limit Theorems for Certain Stochastic Models for Gene Regulatory Networks (with K. Horbacz and H. Wojewódka), AIP Conference Proceedings 1978 (2018), 470051, doi: 10.1063/1.5044121
Limit theorems for a Markov Model of Autoregulated Gene Expression (with K. Horbacz and H. Wojewódka), AIP Conference Proceedings 2116 (2019), 450055, doi: 10.1063/1.5114522
On the Connection between Exponential Ergodicity of a Piecewise Deterministic Markov Process and the Chain Given by its Post-jump locations (with K. Horbacz and H. Wojewódka - Ściążko), AIP Conference Proceedings 2293 (2020), 420056, doi: 10.1063/5.0026519
On the continuous dependence of the stationary distribution of a piecewise deterministic Markov process on its jump intensity (with S.C. Hille, K. Horbacz and H. Wojewódka - Ściążko), AIP Conference Proceedings 2293 (2020), 420083, doi: 10.1063/5.0027213
A note on absolute continuity of stationary distributions of some piecewise-deterministic Markov process (with K. Horbacz and H. Wojewódka - Ściążko), AIP Conference Proceedings 2425, 420015 (2022), doi: 10.1063/5.0081329
A criterion on exponential ergodicity in the bounded-Lipschitz distance for some piecewise-deterministic Markov processes with random switching (with K. Horbacz and H. Wojewódka - Ściążko), AIP Conference Proceedings 2849, 450015 (2023), doi:10.1063/5.0163391
Inne
Rozprawa doktorska: Asymptotyczna stabilność regularnych operatoró Markowa-Fellera z e-własnością na przestrzeniach polskich.
Moje aplikacje do generowania fraktali (dla Windows, spakowane RAR):
Barnsley Fern (generuje fraktal poprzez iterowany układ funkcyjny złożony z czterech transformacji afinicznych, np. Paproć Barnsleya)
Mandelbrot Set (generuje zbiór Mandelbrota)