Distinguishing between fractional Brownian motion with random and constant Hurst exponent using sample autocovariance-based statistics.

Fractional Brownian motion (FBM) is a canonical model for describing dynamics in various complex systems. It is characterized by the Hurst exponent, which is responsible for the correlation between FBM increments, its self-similarity property, and anomalous diffusion behavior. However, recent research indicates that the classical model may be insufficient in describing experimental observations when the anomalous diffusion exponent varies from trajectory to trajectory.

Testing of two-dimensional Gaussian processes by sample cross-covariance function.

In this paper, we address the issue of testing two-dimensional Gaussian processes with a defined cross-dependency structure. Multivariate Gaussian processes are widely used in various applications; therefore, it is essential to identify the theoretical model that accurately describes the data. While it is relatively straightforward to do so in a one-dimensional case, analyzing multi-dimensional vectors requires considering the dependency between the components, which can significantly affect the efficiency of statistical methods.

Divergence-Based Segmentation Algorithm for Heavy-Tailed Acoustic Signals with Time-Varying Characteristics.

Many real-world systems change their parameters during the operation. Thus, before the analysis of the data, there is a need to divide the raw signal into parts that can be considered as homogeneous segments. In this paper, we propose a segmentation procedure that can be applied for the signal with time-varying characteristics.

Identification, Decomposition and Segmentation of Impulsive Vibration Signals with Deterministic Components-A Sieving Screen Case Study.

Condition monitoring is a well-established field of research; however, for industrial applications, one may find some challenges. They are mostly related to complex design, a specific process performed by the machine, time-varying load/speed conditions, and the presence of non-Gaussian noise. A procedure for vibration analysis from the sieving screen used in the raw material industry is proposed in the paper.