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Growth and Structure of Stochastic Sequences

E. Ben-Naim·P. L. Krapivsky
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Abstract

We introduce a class of stochastic integer sequences. In these sequences, every element is a sum of two previous elements, at least one of which is chosen randomly. The interplay between randomness and memory underlying these sequences leads to a wide variety of behaviors ranging from stretched exponential to log-normal to algebraic growth. Interestingly, the set of all possible sequence values has an intricate structure.

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E. Ben-Naim, P. L. Krapivsky. 2002-08-05. Growth and Structure of Stochastic Sequences. https://doi.org/10.1088/0305-4470%2F35%2F41%2F101

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