Joint continuity and a Doob-Meyer type decomposition for renormalized intersection local times
The paper is concerned with a special class of radially symmetric Lévy processes in \(\mathbb{R}^d\) which belong to a stable domain of attraction, and more precisely with their so-called renormalized self-intersection local times. General sufficient conditions for the existence of a jointly continuous version are obtained. The approach relies on a decomposition of Doob-Meyer type which is used to express the \(n\)-fold intersection local time in terms of a lower order intersection local time, and on known results about the continuity of Gaussian chaos processes.
scientific article; zbMATH DE number 1275426