| Title |
Fractional Brownian Vector Field in the framework of Euclidean geometry |
| Authors |
Sakalauskas, Leonidas ; Urbonaitė, Neringa |
| DOI |
10.3390/math14132432 |
| Full Text |
|
| Is Part of |
Mathematics.. Basel : MDPI. 2026, vol. 14, iss. 13, art. no. 2432, p. [1-21].. eISSN 2227-7390 |
| Keywords [eng] |
Brownian fields ; Hurst parameter ; maximum likelihood ; random fields ; variogram |
| Abstract [eng] |
A new fractional Brownian vector field (FBVF) is created for modeling multidimensional and multivariate fractal data. It is shown that the FBVF is a multidimensional and multivariate generalization of the classical Kolmogorov–Wiener process, allowing the distribution of field increments to be defined solely through fractal Euclidean distances between observation points. Conditions are established under which the family of field distributions satisfies the Kolmogorov consistency theorem. Maximum likelihood and variogram-based methods are developed to analytically estimate the mean and covariance of the FBVF, while the Hurst parameter is computed using an one-variable optimization algorithm. A kriging method is constructed for solving prediction problems using observations of fractal data. For computer simulation of field realizations, recursive and kriging-based algorithms are applied. A computational Monte Carlo experiment confirms the reliability of the proposed methods, particularly in accurately estimating the Hurst parameter. Applications to heavy metal concentrations in soil and climate data analysis demonstrate the effectiveness of the model in representing and analyzing multifractal, multidimensional processes. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2026 |
| CC license |
|
