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...l expectation]] of more than three times the [[Standard deviation|standard deviation]]. where $\Phi(\cdot)$ is the distribution function of the standard normal law; whence, in particular, for $k=3$ it follows that

Let $\beta ( t )$, $t \geq 0$, be the standard [[Brownian motion|Brownian motion]] in $\mathbf{R} ^ { d }$ (i.e. the [[Mar The large deviation behaviour of $| W^ { a } ( t ) |$ in the downward direction has been studie

large deviation asymptotics of test statistics under the large deviation asymptotics under the alternative. Each type of

was later called the standard deviation.