Abstract
We characterize stochastic compactness and convergence in distribution of a Lévy process at “large times", i.e., as t→∞, by properties of its associated Lévy measure, using a mechanism for transferring between discrete (random walk) and continuous time results. We thereby obtain also domain of attraction characterisations for the process at large times. As an illustration of the stochastic compactness ideas, semi-stable laws are considered.
Information
Digital Object Identifier: 10.1214/09-IMSCOLL516