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Strong Gaussian approximation for cumulative processesстатья
- Авторы: Bashtova Elena, Shashkin Alexey
- Журнал: Stochastic Processes and their Applications
- Том: 150
- Год издания: 2022
- Издательство: Elsevier BV
- Местоположение издательства: Netherlands
- Первая страница: 1
- Последняя страница: 18
- DOI: 10.1016/j.spa.2022.04.003
- Аннотация: 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.
- Добавил в систему: Баштова Елена Евгеньевна