The local times arise as the density of the occupation measure of a real valued Lévy process. We say x is a favorite point up to time t of a Lévy process if the local time attains its maximum in the space variable. We investigate the asymptotic behavior around zero and in- finity of the time-indexed favorite points. This work extends previous findings by Bass, Griffin, Eisenbaum, Shi, Marcus. The key tool is a generalized Ray-Knight theorem which links the distribution of the local times of symmetric Markov processes with that of some squared Gaussian process. The talk is based on a joint work with B. Li (CCNU) and Y. Xiao (Michigan State)
