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Long memory and self-similar processes

Gennady Samorodnitsky (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

This paper is a survey of both classical and new results and ideas on long memory, scaling and self-similarity, both in the light-tailed and heavy-tailed cases.

Lower quantization coefficient and the F-conformal measure

Mrinal Kanti Roychowdhury (2011)

Colloquium Mathematicae

Let F = f ( i ) : 1 i N be a family of Hölder continuous functions and let φ i : 1 i N be a conformal iterated function system. Lindsay and Mauldin’s paper [Nonlinearity 15 (2002)] left an open question whether the lower quantization coefficient for the F-conformal measure on a conformal iterated funcion system satisfying the open set condition is positive. This question was positively answered by Zhu. The goal of this paper is to present a different proof of this result.

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