Version 1
: Received: 16 May 2023 / Approved: 17 May 2023 / Online: 17 May 2023 (03:38:22 CEST)
How to cite:
Wang, W. Small Values and Chung's Laws of the Iterated Logarithm for Spatial Surface of Operator Fractional Brownian Motion. Preprints2023, 2023051175. https://doi.org/10.20944/preprints202305.1175.v1
Wang, W. Small Values and Chung's Laws of the Iterated Logarithm for Spatial Surface of Operator Fractional Brownian Motion. Preprints 2023, 2023051175. https://doi.org/10.20944/preprints202305.1175.v1
Wang, W. Small Values and Chung's Laws of the Iterated Logarithm for Spatial Surface of Operator Fractional Brownian Motion. Preprints2023, 2023051175. https://doi.org/10.20944/preprints202305.1175.v1
APA Style
Wang, W. (2023). Small Values and Chung's Laws of the Iterated Logarithm for Spatial Surface of Operator Fractional Brownian Motion. Preprints. https://doi.org/10.20944/preprints202305.1175.v1
Chicago/Turabian Style
Wang, W. 2023 "Small Values and Chung's Laws of the Iterated Logarithm for Spatial Surface of Operator Fractional Brownian Motion" Preprints. https://doi.org/10.20944/preprints202305.1175.v1
Abstract
The multivariate Gaussian random fields with matrix-based scaling laws are widely used for inference in statistics and many applied
areas. In such contexts interests are often in symmetry and in the rates of change of spatial surfaces in any given direction. This article analyzes the almost sure sample function behavior for operator fractional Brownian motion, including multivariate fractional Brownian motion. We obtain the estimations of small ball probability and the strongly locally nondeterministic for operator fractional Brownian motion in any given direction. Applying these estimates we obtain Chung's laws of the iterated logarithm for spatial surfaces of operator fractional Brownian motion. Our results show that the precise rates of change of spatial surfaces are completely determined by the self-similarity exponent.
Keywords
operator fractional Brownian motion; small ball probability; operator self-similarity; Chung's law of the iterated logarithm
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
