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Asymptotics for Products of Sums and U-statistics
central limit theorem lognormal distribution products of sums records U-statistics
2009/4/29
The product of subsequent partial sums of independent, identically distributed, square integrable, positive random variables is asymptotically lognormal. The result extends in a rather routine way to ...
Yule process sample path asymptotics
Large deviations random trees branching process fluid limit Yule process
2009/4/22
This paper presents two results on sample paths for the Yule process: one fluid limit theorem and one sample path large deviation result. The main interest is to understand the way large deviation occ...