Generalization of multifractal theory within quantum calculus
Анотація
On the basis of the deformed series in quantum calculus, we gener-alize the partition function and the mass exponent of a multifractal, as well as the average of a random variable distributed over self-similar set. For the partition function, such expansion is shown to be determined by binomial-type combinations of the Tsallis entropies related to manifold deformations, while the mass exponent expansion generalizes the known relation τq = Dq(q − 1). We find equation for set of averages related to ordinary, escort, and generalized probabilities in terms of the deformed expansion as well. Multifractals related to the Cantor binomial set, ex-change currency series, and porous surface condensates are considered as examples.
Класифікація
Ідентифікатори
Рецензії (0)
Написати рецензіюРецензій ще немає. Будьте першим!
Схожі роботи
Recognition of stable distribution with Lévy index<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>close to 2
Схоже за: Financial Risk and Volatility Modeling · Statistical Mechanics and Entropy · Complex Systems and Time Series Analysis
Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem
Схоже за: Financial Risk and Volatility Modeling · Statistical Mechanics and Entropy · Complex Systems and Time Series Analysis
Entropy and alternative entropy functionals of fractional Gaussian noise as the functions of Hurst index
Схоже за: Financial Risk and Volatility Modeling · Statistical Mechanics and Entropy · Complex Systems and Time Series Analysis
Fractional Gaussian Noise: Projections, Prediction, Norms
Схоже за: Financial Risk and Volatility Modeling · Statistical Mechanics and Entropy · Complex Systems and Time Series Analysis
Approximation of multifractional Brownian motion by absolutely continuous processes
Схоже за: Financial Risk and Volatility Modeling · Complex Systems and Time Series Analysis
Exploring frequency of price overreactions in the Ukrainian stock market
Схоже за: Financial Risk and Volatility Modeling · Complex Systems and Time Series Analysis