Strong Gaussian approximation for cumulative processes

Elena Bashtova and Alexey Shashkin

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 1-18

Abstract: We establish the optimal rates of strong approximation by Wiener process for vector-valued cumulative processes. The Komlós–Major–Tusnády bounds are given both in the case when exponential moments exist and for the power moments case. Applications to strong invariance principle for stopped sums and birth and death processes are provided. As a tool we use a maximal inequality for sums over random intervals which is of independent interest.

Keywords: Strong invariance principle; Gaussian approximation; Cumulative processes; Maximal inequalities; Stopped sums; Birth and death processes (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:150:y:2022:i:c:p:1-18

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DOI: 10.1016/j.spa.2022.04.003

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