Convergence in law for certain additive functionals of symmetric stable processes under strong topology (Q1773344)

Let \((X_{t})_{t=0}\) be a symmetric stable process with index \(\alpha\in (1,2]\). \textit{N. Eisenbaum} [in: Séminaire de probabilités XXXI. Lect. Notes Math. 1655, 216--224 (1997; Zbl 0882.60076)] proved a weak convergence result involving \(X\) and its (continuous) local time process. In the special case \(\alpha =2\), when \(X\) is a Brownian motion, \textit{E. Csáki, Z. Shi} and \textit{M. Yor} [in: Limit theorems in probability and statististics. Vol. I, 365--387 (2002; Zbl 1030.60073)] proved another weak convergence result involving\ \(X\) and a fractional derivative of order \(0\) of its Brownian local time. These results were established in the space of continuous functions. The present author extends them to anisotropic Besov spaces.