Discrete-space partial dynamic equations on time scales and applications to stochastic processes |
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Institution: | 1. University of West Bohemia, Faculty of Applied Sciences and NTIS, Univerzitní 22, 306 14 Plzeň, Czech Republic;2. Charles University in Prague, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8, Czech Republic |
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Abstract: | We consider a general class of discrete-space linear partial dynamic equations. The basic properties of solutions are provided (existence and uniqueness, sign preservation, maximum principle). Above all, we derive the following main results: first, we prove that the solutions depend continuously on the choice of the time scale. Second, we show that, under certain conditions, the solutions describe probability distributions of nonhomogeneous Markov processes, and that their time integrals remain the same for all underlying regular time scales. |
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Keywords: | Time scales Partial dynamic equations Stochastic process Nonhomogeneous Markov process Continuous dependence |
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