Growth and structure of stochastic sequences
E Ben-Naim, P L Krapivsky · Journal of Physics A Mathematical and General · 2002
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 behaviours ranging from stretched exponential to log-normal to algebraic growth. Interestingly, the set of all possible sequence values has an intricate structure.