Absolute Continuity of Stable Seminorms
Absolute Continuity of Stable Seminorms
Suppose that $E$ is a complete separable real metric vector space. It is proved that if $X$ is a symmetric $E$-valued $p$-stable random vector, $0 < p < 2$, and $q$ is a lower semicontinuous, a.s. finite seminorm, then the distribution of $q(X)$ is absolutely continuous apart from a possible …