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A simple master Theorem for discrete divide and conquer recurrences

Authors
  • Garet, Olivier
Publication Date
Feb 26, 2019
Source
HAL-UPMC
Keywords
Language
English
License
Unknown
External links

Abstract

The aim of this note is to provide a Master Theorem for some discrete divide and conquer recurrences: $$X_{n}=a_n+\sum_{j=1}^m b_j X_{\lfloor p_j n \rfloor},$$ where the $p_i$'s belong to $(0,1)$. The main novelty of this work is there is no assumption of regularity or monotonicity for $(a_n)$. Then, this result can be applied to various sequences of random variables $(a_n)_{n\ge 0}$, for example such that $\sup_{n\ge 1}\mathbb{E}(|a_n|)<+\infty$.

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