论文标题
免费列维过程的规律性结果
Regularity results for free Lévy processes
论文作者
论文摘要
给定免费添加卷积半群$ \ left（μ_t\右）_ {t \ geq 0} $和概率度量$ν$上的$ \ mathbb {r} $，我们在$ \μ_t\ boxplus c上$ lebesgue conter a lie time $ nime $ contery $ close $ closity $ closity $ conty $ conty $ close $ close contery $ close contery $ r { $ t> 0 $。对于没有此属性的半群，我们找到了在其零零分析的$μ_t\ boxplusν$密度的必要条件。这些结果是通过半群的Lévy度量来量化的，这使得构建许多具体示例变得相当容易。最后，我们表明$μ_t\boxplusν$具有有限数量的连接组件，如果$ \ weft（μ_t\ right）_ {t \ geq 0} $和初始定律$ν$都可以支持。
Given a free additive convolution semigroup $\left(μ_t\right)_{t\geq 0}$ and a probability measure $ν$ on $\mathbb{R}$, we find the necessary and sufficient conditions for the process $μ_t \boxplus ν$ to be Lebesgue absolutely continuous with a positive and analytic density throughout $\mathbb{R}$ at all time $t>0$. For semigroups without this property, we find the necessary and sufficient conditions for the density of $μ_t \boxplus ν$ to be analytic at its zeros. These results are quantified by the Lévy measure of the semigroup, making it fairly easy to construct many concrete examples. Finally, we show that $μ_t \boxplus ν$ has a finite number of connected components in its support if both the Lévy measure of $\left(μ_t\right)_{t \geq 0}$ and the initial law $ν$ do.
