Deterministic chaos has been rigorously and extensively studied by mathematicians and scientists. However, the focus of our book is on the interface between 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 nonlinear dynamics literature is growing almost exponentially, we must stress that, as far as this area is concerned, what we shall present in our book may be regarded as the very minimum coverage. For further coverage, readers may refer to Alligood et al. (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.
KeywordsLyapunov Exponent Stationary Distribution Marginal Distribution Correlation Dimension Trapping Region
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