On different characterizations of a normal distribution
H. van Wiechen (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Mark C. Veraar – Mentor
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Abstract
The normal distribution is a very important distribution in probability theory and statisticsand has a lot of unique properties and characterizations. In this report we look at the proof of two of these characterizations and create counterparts of a normal distribution on abstract spaces, such as vector spaces and groups, which we shall call Gaussians. When we look at R^d, all these Gaussians coincide, along with a Gaussian vector in the normal sense, called multivariate normal. Furthermore, for one Gaussian we prove that it has exponential integrability properties.