Let X = {Xt, t ∈ R+} be a symmetric Lévy process with local time {Lt ; (x, t) ∈ R × R +}. When the Lévy exponent ψ(λ) is regularly varying at zero with index 1 < β ≤ 2, and satisfies some additional regularity conditions, lim t→∞ ∫∞ −∞(L x+1 t − Lt ) dx− E (∫∞ −∞(L x+1 t − Lt ) dx ) t √ ψ−1(1/t) L = (8cψ,1) 1/2 (∫ ∞ −∞ ( Lβ,1 )2 dx )1/2 η, where Lβ,1 = {Lβ,1 ; x ∈ R} denotes the local time, at ...