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Malliavin operators for real-valued Gaussian random variables and their applications
 Kubát, Martin ; Kříž, Pavel (advisor) ; Čoupek, Petr (referee)
In this thesis, we introduce Malliavin Operators. We will focus on derivative, di- vergence and Ornstein-Uhlenbeck operator to study properties of transformed Gaussian random variables. We will explain all concepts in detail and add some typical examples. Then we will use Malliavin operators in the proofs of famous Poincaré inequality and variance expansions. The technique of the last proofs provides a good general approach how to solve similar problems with understanding Malliavin Operators. 1
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