Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1150675 | Journal of Statistical Planning and Inference | 2007 | 14 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Endre Csáki, Miklós CsörgÅ, ZdzisÅaw Rychlik, Josef Steinebach,