Actuarial Mathematic, Second Edition by Browers Gerber Hickman

By Browers Gerber Hickman

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The most important issue concerning atrial fibrillation at this early stage in modeling atrial fibrillation appears not to be which of these models is the right one; at present, all these models have to be regarded as metaphors reproducing only some aspects of the phenomenology of atrial fibrillation. Eventually, the choice of a model should be based upon features t h a t are considered to be the most relevant, but it is not yet clear which these are. For example, some mathematical idealizations t h a t appear to have only minor effects on the local dynamics, may well turn out to be relevant for the specific way in which the spatio-temporal complexity is initialized and sustained in real atria.

For these systems dynamic noise can be treated as observational noise and noise reduc­ tion may prove useful. If the shadowing property does not hold for the system under study, one can still estimate the noise-free dynamics, or 'skeleton,' by the methods proposed by Cheng and Tong (1992) and Chan and Tong (1994). It should not be expected that a time series generated by the estimated noisefree dynamics is similar to the observed time series. To reproduce the features of the original time series the skeleton should be 'clothed' with appropriate dynamical noise.

As a result, a positive value of K2 implies a positive value of R\, so t h a t positive values of K'2 imply chaos. Measures for which Dq varies with q are called multi-fractals, whereas if Dq is constant as a function of q, one speaks of a monofractal. We refer to the papers by Halsey et al. (1986), Paladin and Vulpiani (1987) and Peinke et al. 4. Other Invariants 27 Vaienti (1992b) and Veneziano et d. (1995) for the estimation of the Renyi spectra of dimensions and entropies. , 1994). Apart from the Renyi spectrum of dimensions, other definitions of the di­ mension of measures exist.

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