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Lévy classes and self-normalization. (English) Zbl 0891.60036

Summary: We prove a Chung’s law of the iterated logarithm for recurrent linear Markov processes. In order to attain this level of generality, our normalization is random. In particular, when the Markov process in question is a diffusion, we obtain the integral test corresponding to a law of the iterated logarithm due to Knight.

MSC:

60F15 Strong limit theorems
60G50 Sums of independent random variables; random walks
60J55 Local time and additive functionals
60J45 Probabilistic potential theory
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