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On completeness of random transition counts for Markov chains. II

100%

Palma A.

Probability and Mathematical Statistics

2012

tom Vol. 32, Fasc. 2

203--214

It is shown that the random transition count is complete for Markov chains with a fixed length and a fixed initial state, for some subsets of the set of all transition probabilities. The main idea is to apply graph theory to prove completeness in a more general case than in Palma [5].

On completeness of random transition count for Markov chains

88%

Palma A.

Journal of Applied Analysis

2006

tom Vol. 12, nr 2

249-258

It is shown that the random transition count is complete for Markov chains with a fixed lenght and a fixed lenght and a fixed initial state, for some subsets of the set of all transition probabilities.

Inter-voivodship migration in Poland in the 2000-2020 period based on Markov chain analysis

75%

Palma A. , Kałuża-Kopias D.

Statistics in Transition new series

2024

tom 25

nr 1

93-107

The paper presents the scale and directions of inter-voivodship migration in Poland in selected years of the 2000-2020 period. The study focused on permanent residence migration and aimed to identify areas of migration attractiveness and migration catchment voivodships. To study the stochastic nature of these migrations, a Markov chain model was used, in which the states were voivodships. An important aspect of the study involved determining the properties of the transition probability matrix as well as stationary probability in order to characterise the mechanism of inter-voivodship migrations in the years 2000, 2010 and 2020. Data obtained from Statistics Poland were used in the analysis. The transition probability matrix showed that the states were connected and irreducible to each other, while the stationary probability of migration to Dolnośląskie, Małopolskie, Pomorskie, and Wielkopolskie voivodships increased in 2020 compared to 2000. The analysis of the mechanism of migration in the years 2000, 2010, 2020 indicated that Mazowieckie Voivodship was still the main destination for migrants, with the highest stationary probability reaching 0.18 in 2010.