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In this chapter we study stochastic processes in the presence of jump discontinuity, and discuss the meaning of non-vanishing higher-order Kramers–Moyal coefficients. We describe in details the stochastic properties of Poisson jump processes. We derive the statistical moments of the Poisson process and the Kramers–Moyal coefficients for pure Poisson jump events. Growing evidence shows that continuous stochastic modeling (white noise-driven Langevin equation) of time series of complex systems should account for the presence of discontinuous jump components [1–6]. Such time series have some distinct important characteristics, such as heavy tails and occasionally sudden large jumps.... 

In this chapter we show the equivalence between the Langevin approach and the Fokker–Planck equation, and derive the equation for the statistical moments of the process whose dynamics is described by the Langevin equation. © 2019, Springer Nature Switzerland AG  

In this chapter we study stochastic processes in the presence of jump discontinuity, and discuss the meaning of non-vanishing higher-order Kramers–Moyal coefficients. We describe in details the stochastic properties of Poisson jump processes. We derive the statistical moments of the Poisson process and the Kramers–Moyal coefficients for pure Poisson jump events. Growing evidence shows that continuous stochastic modeling (white noise-driven Langevin equation) of time series of complex systems should account for the presence of discontinuous jump components [1–6]. Such time series have some distinct important characteristics, such as heavy tails and occasionally sudden large jumps.... 

In this chapter we show the equivalence between the Langevin approach and the Fokker–Planck equation, and derive the equation for the statistical moments of the process whose dynamics is described by the Langevin equation. © 2019, Springer Nature Switzerland AG  

In ray-tracing-based propagation modelling, the electromagnetic field at the receiver is obtained by coherent summation of the fields of multipath components. It is therefore crucial to accurately calculate the phase of the electromagnetic field of each ray. In practice, when preparing the plan of the environment for ray tracing simulation, the lateral positions of the walls may not be included accurately in the database. This alters the phases of the fields as well as the delays of arrival of multipath components which may consequently lead to less accurate results. In this study, the sensitivity of ray tracing results to this type of geometrical inaccuracy is investigated through the... 

The plan of the environment used in a ray tracing simulation is not usually in exact accordance with the actual environment plan. Errors on the order of several centimeters may be present in describing the lateral wall positions. Such errors are comparable to the wavelength in indoor wireless applications and hence, can severely alter the phases of multipath components and lead to inaccurate electromagnetic field at the receiver. In this paper, the impact of this type of geometrical errors on the ray tracing results is investigated. Lateral wall positions are considered as random variables to account for possible geometrical errors. The statistical moments of some channel parameters are... 

We propose a blind image steganalysis method based on the Singular Value Decomposition (SVD) of the Discrete Cosine Transform (DCT) coefficients that are revisited in this work. We compute geometric mean, mean of log values, and statistical moments (mean, variance and skewness) of the SVDs of the DCT sub-blocks that are averaged over the whole image to construct a 480-element feature vector for steganalysis. These features are fed to a Support Vector Machine (SVM) classifier to discriminate between stego and cover images. Experimental results show that the proposed method outperforms most powerful steganalyzers when applied to some well-known steganography algorithms  

Vivid banding pattern of the chromosome image is a crucial part for diagnosis in karyotype medical test. Furthermore, thriving computer aided segmentation and classification depend on the initial image quality. In this paper, we propose an adaptive and iterative histogram matching algorithm for chromosome contrast enhancement especially in banding patterns which is one of the most important information laid in chromosome image. Objective histogram, with which the initial image needs to be matched, is created based on processes on the initial image histogram. Calculation of statistical moments of image histogram and determination of parameters in each step of iteration based on these moments... 

An ideal steganographic technique embeds secret information into a carrier cover object with virtually imperceptible modification of the cover object. Steganalysis is a technique to discover the presence of hidden embedded information in a given object. Each steganalysis method is composed of feature extraction and feature classification components. Using features that are more sensitive to information hiding yields higher success in steganalysis. So far, several steganalysis methods have been presented which extract some features from DCT or wavelet coefficients of images. Multi-scale and time-frequency localization of an image is offered by wavelets. However, wavelets are not effective in... 

Steganalysis is a technique to detect the presence of hidden embedded information in a given data. Each steganalyzer is composed of feature extraction and feature classification components. Using features that are more sensitive to data hiding yields higher success in steganalysis. The present paper offers a new universal approach to steganalysis that uses statistical moments of contourlet coefficients as features for analysis. A non-linear SVM classifier is used to classify cover and stego images. The effectiveness of the proposed method is demonstrated by extensive experimental investigations. The proposed steganalysis method is compared with two well known steganalyzers against typical... 

The paper presents an effective algorithm to analyze MR-images in order to recognize Alzheimer's Disease (AD) which appeared in patient's brain. The features of interest are categorized in Features of the Spatial Domain (FSD's) and Features of the Frequency Domain (FFD's) which are based on the first four statistic moments of the wavelet transform. Extracted features have been classified by a multi-layer perceptron Artificial Neural Network (ANN). Before ANN, the number of features is reduced from 44 to 12 to optimize and eliminate any correlation between them. The contribution of this paper is to demonstrate that by using the wavelet transform number of features needed for AD diagnosis has...