Abstract
By using the Ito's calculus, a law of the iterated logarithm is established for the processes with independent increments (PII). LetX = {X t,t ≥ 0} be a PII withEX t = 0,V(t) =EX t2 < ∞ and lim t→∞ V(t) = ∞. If one of the following conditions is satisfied,
(2) Suppose the Levy's measure ofX may be written asV(dt, ds) =F t(dx)dV (t) and there is aσ-finite measureG such thatf |y| ≥x F t(dy) ≤a φ|y|≥x G(dy) and φy 2 G(dy) < ∞, then
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This Project is supported by the National Natural Science Foundation of China.
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Wang, J. A law of the iterated logarithm for processes with independent increments. Acta Mathematicae Applicatae Sinica 10, 59–68 (1994). https://doi.org/10.1007/BF02006259
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DOI: https://doi.org/10.1007/BF02006259