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Recurrence properties of Processes with stationary independent increments

Published online by Cambridge University Press:  09 April 2009

J. F. C. Kingman
J. F. C. Kingman
Affiliation:
University of Cambridge and Western Australia
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Let X1, X2,…Xn, … be independent and identically distributed random variables, and write . In [2] Chung and Fuchs have established necessary and sufficient conditions for the random walk {Zn} to be recurrent, i.e. for Zn to return infinitely often to every neighbourhood of the origin. The object of this paper is to obtain similar results for the corresponding process in continuous time.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 2 , May 1964 , pp. 223 - 228
Copyright
Copyright © Australian Mathematical Society 1964

References

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[2]Chung, K. L., and Fuchs, W. H. J., On the distribution of values of sums of random variables, Mem. Amer. Math. Soc. 6 (1951) 1–12.Google Scholar
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[5]Kingman, J. F. C., Random walks with spherical symmetry, Acta. Math. 109 (1963) 11–53.CrossRefGoogle Scholar
[6]Loève, M., Probability theory, (van Nostrand, 1963).Google Scholar