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Curved Chaotic Map Time Series Models and Their Stochastic Reversals
Author(s) -
Lawrance A. J.,
Spencer N. M.
Publication year - 1998
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00110
Subject(s) - mathematics , chaotic , lyapunov exponent , stochastic modelling , series (stratigraphy) , stochastic process , invariant (physics) , statistical physics , logistic map , statistics , computer science , paleontology , physics , artificial intelligence , mathematical physics , biology
This paper considers two types of chaotic map time series models, including the well‐known tent, logistic and binary‐shift maps as special cases; these are called curved tent and curved binary families. Deterministic behaviour is investigated by invariant distributions, Lyapunov exponents, and by serial dependency. Stochastic time reversal of the families is shown to produce models which have a broader range of stochastic and chaotic properties than their deterministic counterparts. The marginal distributions may have concentrations and restricted supports and are shown to be a non‐standard class of invariant distribution. Dependenc y is generally weaker with the reversed stochastic models. The work gives a broad statistical account of deterministic and stochastically reversed map models, such as are emerging in random number generation, communica tion systems and cryptography