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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Completeness of the Kantorovich-Rubinstein metric
 Picek, Radovan ; Seidler, Jan (advisor) ; Maslowski, Bohdan (referee)
In the thesis the Kantorovich-Rubinstein metric in the space of Borel probability me- asures with a finite first moment on a separable complete metric space is studied. Its completeness is proved and convergence of sequences is characterized using elementary tools in Chapter 3. The proofs rely on results about the Dudley metric for weak conver- gence of probability measures, which are dealt with in Chapters 1 and 2. 1
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Optimal risk sensitive control in radical chains
 Picek, Radovan ; Dostál, Petr (advisor) ; Maslowski, Bohdan (referee)
In the first segment this thesis deal with Markov chains with discreet time and a finite set of states. Subsequently there is introduced valuation of transitions and a possibility of controlling these chains. Yields from valuation of transitions are then appointed to exponential utility funcion and discounted to the begining. Afterwards there is estab- lished Howard's iterative algorithm, which finds optimal control. The control is optimal amongst homogeneous and non-homogeneous controls. In the second segment, Markov chains are generalized to so called radical chains, again with discreet time and a finite set of states. The generalization is executed by adding an opportunity of choosing radical decisions, which take place out of real time. Howard's iterative algorithm is modified for this more general case. The control found by the algorithm is optimal amongst homoge- neous and non-homogeneous controls. 1
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2 Picek, Radomír
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