Strong Gaussian approximation for cumulative processes
نویسندگان
چکیده
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 case when exponential moments exist and power case. Applications to invariance principle stopped sums birth death processes provided. As a tool we use maximal inequality over random intervals which is independent interest.
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2022
ISSN: ['1879-209X', '0304-4149']
DOI: https://doi.org/10.1016/j.spa.2022.04.003