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arXiv · 1610.02700

Invariance principles for random sums of random variables

Gane Samb Lo
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Abstract

This note investigates invariance principles for sums of N(nt) iid radom variables, where n is an integer, t is a positive real number and N(u) is a stochastic process with nonnegative integer values. We show that the sequence of sums of these random variables denoted S(n,t), when appropriately centered and normalized, weakly converges to a Gaussian process. We give sufficient conditions depending on the expectation of N(nt) which allows to rescale S(n,t) into a stochastic S(n,a(t)) weakly converging to a Brownian motion.

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Gane Samb Lo. 2016-10-09. Invariance principles for random sums of random variables. https://arxiv.org/abs/1610.02700

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