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Mixing processes with finite alphabet
Vostal, Ondřej ; Kupsa, Michal (advisor) ; Dostál, Petr (referee)
An introduction to the theory of mixing of random processes is presented. The aim of this introduction is to be eventually able to separate general random processes, markov chains and markov chains with finite alphabet into groups which mix differently. The introduction is made complete by examples. We show, that for general processes those groups are separate, for markov chains some coincide, and for markov chains with finite alphabet all coincide. Powered by TCPDF (www.tcpdf.org)
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Continuous Time Linear Quadratic Optimal Control
Vostal, Ondřej ; Maslowski, Bohdan (advisor) ; Pawlas, Zbyněk (referee)
We partially solve the adaptive ergodic stochastic optimal control problem where the driving process is a fractional Brownian motion with Hurst parameter H > 1/2. A formula is provided for an optimal feedback control given a strongly consistent estimator of the parameters of the controlled system is avail- able. There are some special conditions imposed on the estimator which means the results are not completely general. They apply, for example, in the case where the estimator is independent of the driving fractional Brownian motion. In the course of the thesis, construction of stochastic integrals of suitable determinis- tic functions with respect to fractional Brownian motion with Hurst parameter H > 1/2 over the unbounded positive real half-line is presented as well. 1
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Mixing processes with finite alphabet
Vostal, Ondřej ; Kupsa, Michal (advisor) ; Dostál, Petr (referee)
An introduction to the theory of mixing of random processes is presented. The aim of this introduction is to be eventually able to separate general random processes, markov chains and markov chains with finite alphabet into groups which mix differently. The introduction is made complete by examples. We show, that for general processes those groups are separate, for markov chains some coincide, and for markov chains with finite alphabet all coincide. Powered by TCPDF (www.tcpdf.org)
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How True is the True Money Supply?
Vostal, Ondřej ; Svoboda, Miroslav (advisor) ; Hurník, Jaromír (referee)
The Austrian economists hold that the so called true money supply is theoreticaly superior to the classical M1, M2 and M3. Using the data from the Czech Republic I verify in my thesis whether it really could be the case. The true money supply is the sum of the amount of cash and goods (cash equivalents) which could be redeemed during a period not exceeding the horizon specified at a fixed rate known in advance in cash. In addition, most market participants have to think that the amount of cash available for the purpose of such exchange is unlimited. Several true money supplies, that differ in the horizons of the included cash equivalents, are constructed based on the Czech National Bank (ČNB) data spanning the years from 2002 to 2012. For the comparison of the true money supplies and the M an elementary model is used based on the equation of exchange. The main finding is that the indicators don't considerably differ. Thus it seems that the true money supplies and M are practically the same. For all the indicators, however, the estimates of the coefficient of the model are significantly different from the quantitative theory of money predictions. That's why the results are to be interpreted with caution.
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