Multidimensional central limit theorem for sums of functions of the trajectories of endomorphisms
- Авторлар: Dubrovin V.1, Gabbasov F.1, Chebakova V.1
-
Мекемелер:
- Department of System Analysis and Information Technologies
- Шығарылым: Том 37, № 4 (2016)
- Беттер: 409-417
- Бөлім: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198012
- DOI: https://doi.org/10.1134/S1995080216040053
- ID: 198012
Дәйексөз келтіру
Аннотация
We study the rate of convergence in the central limit theorem for vector-valued sequences generated by endomorphisms of a multidimensional torus. In the proved theorem for sums of functions of the trajectories of endomorphisms of s-dimensional Euclidean space it is obtained almost optimal rate of convergence to the normal distribution. In the proof we use “method of successive approximations”, developed by us earlier (see Dubrovin V.T., Moskvin D.A. Theory of Probability & Its Applications, 1980, V. 24, Is. 3, P. 560–571) to prove limit theorems taking into account the rate of convergence for the sums of functions of sequences that satisfy a mixing condition.
Авторлар туралы
V. Dubrovin
Department of System Analysis and Information Technologies
Email: vchebakova@mail.ru
Ресей, Kremlevskaya ul. 18, Kazan, Tatarstan, 420008
F. Gabbasov
Department of System Analysis and Information Technologies
Email: vchebakova@mail.ru
Ресей, Kremlevskaya ul. 18, Kazan, Tatarstan, 420008
V. Chebakova
Department of System Analysis and Information Technologies
Хат алмасуға жауапты Автор.
Email: vchebakova@mail.ru
Ресей, Kremlevskaya ul. 18, Kazan, Tatarstan, 420008
![](/img/style/loading.gif)