On the convergence of stochastic Fibonacci series Authors
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Дата
2025
Автори
Науковий керівник
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Видавець
Igor Sikorsky Kyiv Polytechnic Institute
Анотація
One very spesific case of linear second-order autoregressive sequence of random variables, the so-called stochastic Fibonacci sequence, is considered. For a random series, whose terms are properly normed partial sums of elements of the Fibonacci sequence, we study assumptions which garantee almost sure convergence of the introduced series. Obtained result is quite simple and understandable. In partcular, it implies that the Strong Law of Large Numbers for the Fibonacci sequence holds true.
Опис
Ключові слова
linear autoregression models, Strong Law of Large Numbers, sums of independent random variables, almost sure convergence of random series, лiнiйнi авторегресiйнi моделi, посилений закон великих чисел, суми випадкових величин, збiжнiсть майже напевно випадкових рядiв
Бібліографічний опис
Ilienko, M. K. On the convergence of stochastic Fibonacci series / M. K. Ilienko, L. A.Runovska // Mathematics in Modern Technical University. – 2025. – Vol. 2025, No 1. – P. 43-49. – Bibliog.: 8 ref.