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We present a exactly soluble model for financial time series that mimics the long range volatility correlations known to be present in financial data. Although our model is asymptotically 'monofractal' by construction, it shows apparent multiscaling as a result of a slow crossover phenomenon on finite time scales. Our results suggest that it might be hard(More)
Grünbaum introduced measures of symmetry for convex bodies that measure how far a given convex body is from a centrally symmetric one. Here, we introduce new measures of symmetry that measure how far a given convex body is from one with " enough symmetries ". To define these new measures of symmetry, we use affine covariant points. We give examples of(More)
We elaborate on the use of shadow systems to prove a particular case of the conjectured lower bound of the volume product P(K) = min z∈int(K) |K|||K z |, where K ⊂ R n is a convex body and K z = {y ∈ R n : (y − z) · (x − z) 1 for all x ∈ K} is the polar body of K with respect to the center of polarity z. In particular, we show that if K ⊂ R 3 is the convex(More)
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