Titlebook: Chaos: A Statistical Perspective; Kung-Sik Chan,Howell Tong Book 2001 Springer-Verlag New York 2001 correlation.deterministic chaos.dynami

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Modeling collaboration of profit centers be regarded as the very minimum coverage. For further coverage, readers may refer to Alligood . (1997), Kantz and Schreiber (1997) and others; see the Notes at the end of this chapter. These concepts will be used to motivate Chapter 3, which addresses stochastic processes.

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Deterministic Chaos, be regarded as the very minimum coverage. For further coverage, readers may refer to Alligood . (1997), Kantz and Schreiber (1997) and others; see the Notes at the end of this chapter. These concepts will be used to motivate Chapter 3, which addresses stochastic processes.

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Chaos and Stochastic Systems,cal system, which treats the states as random and describes the transition probabilities from the initial state to the later states. A natural way of characterising the ‘driving force’ behind a stochastic dynamical system is to introduce ., also known as ..

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0172-7397 initial-value sensitivity is a fundamental source of random­ ness. For statisticians working within the traditional statistical framework, the task of critically assimilating randomness generated by a purely de­ terministic system, often known as chaos, is an intellectual challenge. Like some other

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Introduction and Case Studies,petuated in some popular accounts of deterministic chaos theory, from which they might form the impression that the theory attempts to explain almost all random phenomena by purely deterministic systems. They tend to take their leave at this point because their training has convinced them of the limitations of determinism in analysing real data.

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Introduction and Case Studies,actions. Some statisticians might find chaos — the notion totally alien, and even suspicious. They might have heard or overheard one or two claims perpetuated in some popular accounts of deterministic chaos theory, from which they might form the impression that the theory attempts to explain almost

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Deterministic Chaos,etween statistics and chaos. Thus, instead of presenting a formal account here, we shall adopt an informal approach in which we illustrate some basic concepts of deterministic chaos through a few examples. A more systematic account is relegated to Appendix A for interested readers. Because the nonli

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Chaos and Stochastic Systems,on law, i.e. the dynamics, is assumed to be known precisely and the states are assumed to be free from any errors, such as measurement errors, rounding errors, etc. In reality, such assumptions are rarely satisfied. We should therefore extend the deterministic dynamical system to a stochastic dynami

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