Law of the iterated logarithm for oscillating random walks conditioned to stay non-negative. (Q2574613)

The authors prove that under a \(3+\delta \) moment condition (where \(\delta >0\)) there exists a ``Hartman-Winter'' law of the iterated logarithm for random walks conditioned to stay non-negative. They also prove that under a second order moment assumption the conditioned random walk eventually grows faster than \(n^{1/2}(\log n)^{-(1+\varepsilon )}\) for any \(\varepsilon >0\) and yet slower than \(n^{1/2}(\log n)^{-1}\).