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Теория вероятн. и ее примен., 2000, том 45, выпуск 2, страницы 289–311 (Mi tvp464)  

Эта публикация цитируется в 89 научных статьях (всего в 89 статьях)

Superposition of Ornstein–Uhlenbeck type processes

O. E. Barndorff-Nielsen

Institute of Mathematics, University of Aarhus, Denmark

Аннотация: В терминах интегралов по независимо “рассеянным” случайным мерам, построен класс суперпозиций процессов Орнштейна–Уленбека. При определенных условиях результирующие процессы обладают свойством сильного последействия. При интегрировании суперпозиции приводят к кумулятивным процессам со стационарными приращениями, и определено интегрирование по процессам такого рода. Переход к пределу дает процессы, которые в случае квадратичной интегрируемости являются самоподобными (автомодельными) с показателем 2 и имеют стационарные приращения. Некоторые другие из предельных процессов являются устойчивыми и самоподобными (автомодельными) со стационарными приращениями.

Ключевые слова: процессы Орнштейна–Уленбека, процессы Леви, суперпозиции, кумулятивные процессы, самоподобие (автомодельность), сильное последействие.

DOI: https://doi.org/10.4213/tvp464

Полный текст: PDF файл (942 kB)

Англоязычная версия:
Theory of Probability and its Applications, 2001, 45:2, 175–194

Реферативные базы данных:

Поступила в редакцию: 04.03.1999
Язык публикации: английский

Образец цитирования: O. E. Barndorff-Nielsen, “Superposition of Ornstein–Uhlenbeck type processes”, Теория вероятн. и ее примен., 45:2 (2000), 289–311; Theory Probab. Appl., 45:2 (2001), 175–194

Цитирование в формате AMSBIB
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\paper Superposition of Ornstein--Uhlenbeck type processes
\jour Теория вероятн. и ее примен.
\yr 2000
\vol 45
\issue 2
\pages 289--311
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\jour Theory Probab. Appl.
\yr 2001
\vol 45
\issue 2
\pages 175--194
\crossref{https://doi.org/10.1137/S0040585X97978166}
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  • Теория вероятностей и ее применения Theory of Probability and its Applications
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