A1048
Title: Multidimensional fractional Brownian motion: From construction to analysis
Authors: Michal Balcerek - Wroclaw University of Science and Technology (Poland) [presenting]
Abstract: The aim is to introduce a novel construction of two-dimensional fractional Brownian motion (2d fBm) that explicitly captures both anisotropic scaling and cross-component dependencies using a matrix-valued Hurst operator and correlated Gaussian noise. Two distinct models are proposed: Causal and well-balanced 2d fBm, differing in their cross-covariance structures. The theoretical properties of such models (both in time and frequency domains) are introduced, and those are compared to the ones obtained from the numerical simulations. Particular attention is given to how variations in the Hurst parameters and noise correlation structures manifest in observed behavior, and how those influence data analysis.
