2021/04/18 by Philip Broadbridge, Broadbridge, Phil, Ravindi Nanayakkara +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60G15 #60G22 #60G60 #62M40 #83F05 #FOS: Physical sciences #Financial Risk and Volatility Modeling #General Physics (physics.gen-ph) #Scientific Research and Discoveries #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2104.13945
openalex publication_date 2021/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies random fields on the unit sphere. Traditionally, isotropic Gaussian random fields are considered as the underlying statistical model of the cosmic microwave background (CMB) data. This paper discusses the generalized multifractional Brownian motion and its pointwise Hölder exponent on the sphere. The multifractional approach is used to investigate the CMB data from the Planck mission. These data consist of CMB radiation measurements at narrow angles of the sky sphere. The obtained results suggest that the estimated Hölder exponents for different CMB regions do change from location to location. Therefore, CMB data are multifractional. Then the developed methodology is used to suggest two approaches for detecting regions with anomalies in cleaned CMB maps.