On Vervaat and Vervaat-error type processes for partial sums and renewals

Details On Vervaat and Vervaat-error type processes for partial sums and renewals On Vervaat and Vervaat-error type processes for partial sums and renewals

2004-01-06

arxiv.org/abs/math/0401041v1

Mathematics

Probability

17 pages, 2 figures

Scientific paper

We study the asymptotic behaviour of stochastic processes that are generated by sums of partial sums of i.i.d. random variables and their renewals. We conclude that these processes cannot converge weakly to any nondegenerate random element of the space $D[0,1]$. On the other hand we show that their properly normalized integrals as Vervaat-type stochastic processes converge weakly to a squared Wiener process. Moreover, we also deal with the asymptotic behaviour of the deviations of these processes, the so-called Vervaat-error type processes.

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