Two strong limit theorems for processes with independent increments
نویسندگان
چکیده
منابع مشابه
Central limit theorems for the L 2 norm of increments of local times of Lévy processes ∗
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 ...
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ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 1982
ISSN: 0047-259X
DOI: 10.1016/0047-259x(82)90013-6