Embeddability of infinitely divisible distributions on Lie groups (Q6623992)

Given a locally compact group \(G\), a probability measure \(\mu\) on \(G\) is infinitely divisible if, for each \(n\in\mathbb{N}\), there exists a probability measure \(\lambda_n\) on \(G\) such that the \(n\)-fold convolution of \(\lambda_n\) is \(\mu\). Also, \(\mu\) is embeddable if there exists a one-parameter convolution semigroup \(\{\mu_t\}_{t\geq0}\) with \(\mu_1=\mu\). While every embeddable probability measure is infinitely divisible (with the choice \(\lambda_n=\mu_{1/n}\)), the converse is not true. The present paper offers a survey of results in this area, and in particular on conditions under which it is known that a probability measure on a connected Lie group is embeddable, and related results.