New answers tagged

11

I will answer a simplified version, so leave the generalization as an exercise. Let $Z$ be a standard normal random variable so $X=e^Z$ is standard lognormal. Since $X>0 $ we have $Y=\frac1{1+X}$ is in the unit interval. Let $\phi, \Phi$ be the density and cdf (cumulative distribution ) functions of the standard normal, then we find $$ \...


1

This is rather sophisticated and not a one-line proof one could present here. Anyway, here is some (my) intuition. The circle has a Lie-group structure and therefore one can in a natural way talk about random walks on a circle. Then mimicing the strategy of Donskers invariance theorem on the real line, i.e. interplolate, rescale etc, you will be able to ...


Top 50 recent answers are included