2015/08/29 by Ming Liao, Liao, Ming
Mathematics · #60B15 #Advanced Algebra and Geometry #FOS: Mathematics #Geometry and complex manifolds #Mathematical Analysis and Transform Methods #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1508.07476
openalex publication_date 2015/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study (weakly) continuous convolution semigroups of probability measures on a Lie group G or a homogeneous space G/K, where K is a compact subgroup. We show that such a convolution semigroup is the convolution product of its initial measure and a continuous convolution semigroup with initial measure at the identity of G or the origin of G/K. We will also obtain an extension of Dani-McCrudden's result on embedding an infinitely divisible probability measure in a continuous convolution semigroup on a Lie group to a homogeneous space.