Abstract
An integral test is obtained to determine whether P{X t ≤ βt i.o. } is 0 or 1 where t −1 β t is nondecreasing and X t is a subordinator belonging to a large class which contains the stable subordinators. This generalizes the results of Breiman for the stable subordinators.
Research supported in part by N.S.F. Grants DMS-8603437 and DMS-8902581
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References
L. Breiman, A delicate law of the iterated logarithm for non-decreasing stable processes, Ann. Math. Statist. 39 (1968), 1818–1824 (Correction 41 (1970) 1126 )
A. Dvoretzky and P. Erdös, Some problems on random walk in space, Proc. Second Berkeley Symp. Math. Statist. Probab., 353–367, Univ. California Press, Berkeley, CA, 1951
N.C. Jain and W.E. Pruitt, Lower tail probability estimates for subordinators and nondecreasing random walks, Ann. Probab. 15 (1987), 75–101
W.E. Pruitt, The rate of escape of random walk,Ann. Probab. 18(1990), 1417–1461.
F. Spitzer, Some theorems concerning 2-dimensional Brownian motion, Trans. Amer. Math. Soc. 87 (1958), 187–197
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© 1991 Springer Science+Business Media New York
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Pruitt, W.E. (1991). An Integral Test for Subordinators. In: Durrett, R., Kesten, H. (eds) Random Walks, Brownian Motion, and Interacting Particle Systems. Progress in Probability, vol 28. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0459-6_22
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DOI: https://doi.org/10.1007/978-1-4612-0459-6_22
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