We proof a limit theorem for the
-modulus of continuity of Brownian
local time. As special cases for
p=2 and
p=3, we obtain previous results by
Chen et al. (Ann. Prob. 38, 2010, no. 1) and Rosen~(Stoch. Dyn. 11, 2011, no.
1), which were later reproven by Hu and Nualart~(Electron. Commun. Probab. 14,
2009; Electron. Commun. Probab. 15, 2010) and Rosen~(S\'eminaire de
Probabilit\'es XLIII,
... [Show full abstract] Springer, 2011). In comparison to the previous methods of
proof, we follow a fundamentally different approach by exclusively working in
the space variable of the Brownian local time, which allows to give a unified
argument for arbitrary integer power p. The main ingredients are Perkins'
semimartingale decomposition, the Kailath-Segall identity and an asymptotic
Ray-Knight Theorem by Pitman and Yor.