Time evolution in distributions of Lévy processes (Q1893924)

By the following definition the author introduces the direction of his investigations in the theory of Lévy processes: Property A is of time-evolution type if there is a Lévy process \((X_t)\) such that, for some \(t_1 > 0\) and \(t_2 > 0\), \(\mu_{t_1} (\cdot)\) has property A and \(\mu_{t_2}(\cdot)\) does not have property A \((\mu_t(B) = P(X_t \in B))\). Otherwise property A is of no-time-evolution type. After recalling some properties being of time-evolution type or not, the considerations are focused on the case: property \(\text{A} := \) ``modality'' (unimodality, strictly unimodality, strictly-\(n\)-modality). Then different sets of conditions are found under which different variations of time evolutions of modality happen. The considerations are often reduced to subordinators or compound Poisson processes.