Wavelet entropy and fractional Brownian motion time series

Characterization of the Laser Propagation Through Turbulent Media by Quantifiers Based on Wavelet Transform

1 The propagation of a laser beam through turbulent media is modeled as a fractional Brownian motion (fBm). Time series corresponding to the center position of the laser spot (coordinates x and y) after traveling across air in turbulent motion, with different strength, are analyzed by the wavelet theory. Two quantifiers are calculated, the Hurst exponent and the Normalized Total Wavelet Entropy...

6 Wavelet entropy of stochastic processes

We compare two different definitions for the wavelet entropy associated to stochastic processes. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise (−1 < α < 1) and the fractional Brownian motion (1 < α < 3) are assessed. We find out that NTWS family performs better as a characterization method for these stochastic processes.

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

n-Order and maximum fuzzy similarity entropy for discrimination of signals of different complexity: Application to fetal heart rate signals

This paper presents two new concepts for discrimination of signals of different complexity. The first focused initially on solving the problem of setting entropy descriptors by varying the pattern size instead of the tolerance. This led to the search for the optimal pattern size that maximized the similarity entropy. The second paradigm was based on the n-order similarity entropy that encompass...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion