Total variation of Gaussian processes and local times of associated Levy processes

摘要

Results of Taylor and Marcus and Rosen on the total variation of Gaussian processes and local times of associated symmetric stable processes are extended to a large class of symmetric Levy processes. In this extension, the increments variance sigma2(h) of the Gaussian process is generalized to a regularly varying function with index 0 < alpha < 2. The total variation function ϕ(·) is generalized to 4x=r -1x2log +log1/x . where sh=b hrh =bhha exp1h eu udu. where 0 < alpha < 1, limh →0beta(h) = 1 and limu →0 epsilon(u) = 0.