Is bullet point one true, or is there a condition that I’m not assuming? E.g if $V$ is the constant $0$ random variable and $X$ is $N(0, 1)$ then the limit result holds, but a Gaussian is neither heavy- nor long-tailed.
I’m also assuming V is not bounded above.
Is bullet point one true, or is there a condition that I’m not assuming? E.g if $V$ is the constant $0$ random variable and $X$ is $N(0, 1)$ then the limit result holds, but a Gaussian is neither heavy- nor long-tailed.
I’m also assuming V is not bounded above.