Limit theorem and LIL for some additive functionals associated to fBm and Riemann-Liouiville process

Mohamed Ait Ouahra; Abderrahim Aslimani; Mhamed Eddahbi; Mohamed Mellouk

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arXiv · 2302.05141

Limit theorem and LIL for some additive functionals associated to fBm and Riemann-Liouiville process

Mohamed Ait Ouahra·Abderrahim Aslimani·Mhamed Eddahbi·Mohamed Mellouk

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Abstract

In this paper, we first establish a strong approximation version for the first order limit theorem of some additive functionals related to two non-Markovian Gaussian processes: the fractional Brownian motion (fBm) and the Riemann-Liouville process. As application, we give the law of iterated logarithm of the same additive functionals associated to this two processes

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Mohamed Ait Ouahra, Abderrahim Aslimani, Mhamed Eddahbi, Mohamed Mellouk. 2023-02-10. Limit theorem and LIL for some additive functionals associated to fBm and Riemann-Liouiville process. https://arxiv.org/abs/2302.05141

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