Definition:Sub-Gaussian Distribution

Definition
The distribution of a random variable $X$ with expectation $\mu = \expect X$ is called sub-Gaussian there exists a $\sigma \in \R_{>0}$ such that:


 * $\expect {e^{\lambda \paren {X - \mu} } } \le e^{\sigma^2 \lambda^2 / 2}$

for all $\lambda \in \R$.